Publications -- Jie Shen

Publications of Jie Shen

Books

Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations (by Mohsen Zayernouri, Li-Lian Wang, and George Krniadakis, Cambridge University Press, Nov. 2024).

Spectral Methods: Algorithms, Analysis and Applications (Springer Series in Computational Mathematics, V. 41) (by Jie Shen, Tao Tang and Li-Lian Wang, Springer, Aug. 2011), Erratum and the associated Matlab codes.

Spectral and High-Order Methods with Applications (by Jie Shen and Tao Tang, Science Press of China, 2006); Erratum and Matlab & Fortran codes for the book. You may purchase the book at www.amazon.com or at www.amazon.com.cn.

Papers

Disclaimer: The copyrights of these papers belong to the publishers of the journals. The papers may be downloaded for personal use only. Any other use requires prior permission of the authors and the publishers.

2024 ---

(with Buyang Li, Zongze Yang and Yanrong Zhang) Efficient energy stable schemes for incompressible flows with variable density. J. Comput. Phys. 517:113365, 2024.

(with Chen Liu, Beatrice Riviere, and Xiangxiong Zhang) A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system. SIAM J. Sci. Comput. 46:A1923-A1948, 2004.

(with Desong Kong, Lilian Wang and Shuhuang Xiang) Eigenvalue Analysis and Application of the Legendre Dual-Petrov-Galerkin Methods for Initial Value Problems. Adv. Comput. Math. 50:97, 2024.

(with Fukeng Huang) On a new class of BDF and IMEX schemes for parabolic type equations. SIAM J. Numer. Anal. 62:1609-1637, 2024.

(with Xinyu Liu and Nan Zheng) Efficient energy stable numerical schemes for Cahn-Hilliard equations with dynamical boundary conditions. J. Comput. Phys. 509:113037, 2024.

(with Fukeng Huang) A class of IMEX schemes and their error analysis for the Navier-Stokes Cahn-Hilliard system. Annals Math. Sci. Appl. 9(1):185-235, 2024.

(with Xueling Huang) Efficient numerical schemes for a two-species Keller-Segel model and investigation of its blowup phenomena in 3D. Acta Applicandae Mathematicae, 190:10, 2024.

(with Ziqi Ma, Zhiping Mao) Efficient and stable sav-based methods for solving the gradient flows arising from deep learning. J. Comput. Phys. 505:112911, 2024.

(with Jiahao Zhang, Shiheng Zhang, and Guang Lin) Energy-Dissipative Evolutionary Deep Operator Neural Networks. J. Comput. Phys. 498:112638, 2024.

(with Xinyu Liu and Xiangxiong Zhang) A simple GPU implementation of spectral-element methods for solving 3D Poisson type equations on cartesian meshes. arXiv.2310.00226, Oct. 2023. A demonstration on how to run the code

2023

(with Fukeng Huang) Stability and error analysis of a second order consistent splitting scheme for the Navier-Stokes equations. SIAM J. Numer. Anal. 61:2408-2433, 2023.

(with Can Huang) Stability and convergence analysis of a fully discrete semi-implicit scheme for stochastic Allen-Cahn equations with multiplicative noise. Math. Comp. 92:2685--2713, 2023.

(with Xiangyu Bai, Jiebao Sun, Wenjuan Yao, Zhichang Guo) A Ginzburg-Landau $H^{-1}$ model and its SAV algorithm for image inpainting. J. Sci. Comput. 96:40, 2023.

(with Xiaoli Li) Error estimate of a consistent splitting GSAV scheme for the Navier-Stokes equations. Appl. Numer. Math. 188:62-74, 2023.

(with Yanrong Zhang) A new class of efficient SAV schemes with Lagrange multipliers for dissipative systems with global constraints. East Asian J. Appl. Math. 13:550-575, 2023.

(with Yana Di, Yuheng Ma and Jiwei Zhang) A variable time-step IMEX-BDF2 SAV scheme and its sharp error estimate for the Navier-Stokes equations. ESAIM: Math. Model. Numer. Anal. 57:1143-1170, 2023.

(with Xueling Huang) Bound/positivity preserving SAV schemes for the Patlak-Keller-Segel-Navier-Stokes system. J. Comput. Phys. 480:112034, 2023.

(with Yiqi Gu) A fictitious domain spectral method for solving the Helmholtz Equation in exterior domains. J. Sci. Comput. 94:46, 2023.

(With Xinyu Liu and Xiangxiong Zhang) An efficient and robust SAV based algorithm for discrete gradient systems arising from optimizations. SIAM J. Sci. Comput. 45:A2304--A2324, 2023.

(with Sheng Chen) Log orthogonal functions in semi-infinite intervals: approximation results and applications. SIAM J. Numer. Anal. 61:110-134, 2023.

(with Qing Cheng) Length preserving numerical schemes for Landau-Lifshitz equation based on Lagrange multiplier approaches SIAM J. Sci. Comput. 45:A530-A553, 2023.

(with Zhe Yu) Efficient SAV--Hermite methods for the Nonlinear Dirac Equation. DCDS-B 28:3428-3452, 2023.

(with Xiaoli Li) Error analysis of a fully discrete consistent splitting mac scheme for time dependent stokes equations. J. Comput. Appl. Math. 41:114892, 2023.

2022

(with Juan M. Lopez, Bruno D. Welfert and Ke Wu) Boundary-confined waves in a librating cube. J. Fluid Mech. vol. 952, R2, doi:10.1017/jfm.2022.934, 2022.

(with Jingwei Hu, Xiaodong Huang and Haizhao Yang) A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions. SIAM J. Sci. Comput. 44:A1497-A1524, 2022.

(with Rui Wang, Yanzhou Ji and Long-Qing Chen) Application of Scalar Auxiliary Variable Approach to Phase-Field Equations Comput. Mat. Sci., 212:111556, 2022.

(with Wenbin Chen and Qianqian Liu) Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system. Inter. J. Numer. Anal. Model., 19:275-298, 2022.

(with Fukeng Huang and Ke Wu) Bound/positivity preserving and unconditionally stable schemes for a class of fourth order nonlinear equations. J. Comput. Phys. 460:111177, 2022.

(with Xiaoli Li) On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of two-phase incompressible flows. Math. Models & Methods Appl. Sci., 32:457-495, 2022.

(with Fukeng Huang and Ke Wu) A new class of higher-order decoupled schemes for the incompressible Navier-Stokes equations and applications to rotating dynamics. J. Comput. Phys. 458:111097, 2022.

(with Yanrong Zhang) A generalized SAV approach with relaxation for dissipative systems. J. Comput. Phys., 464:111311, 2022.

(with Qing Cheng) A new Lagrange multiplier approach for constructing structure preserving schemes, II. bound preserving. SIAM J. Numer. Anal., 60:970-998, 2022.

(with Qing Cheng) A new Lagrange multiplier approach for constructing structure preserving schemes, I. positivity preserving. Comp. Methods Appl. Math. Eng. 391:114585, 2022.

(with Xiangxiong Zhang) Discrete Maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation. Comm. Math. Sci. 20:1409-1436, 2022.

(with Xiaoli Li and Weilong Wang) Stability and error analysis of IMEX SAV schemes for the magneto-hydrodynamic equations. SIAM J. Numer. Anal. 60:1026-1054, 2022.

(with Nan Zheng) Efficient and Unconditional Energy Stable Schemes for the Micropolar Navier-Stokes Equations. CSIAM Trans. Appl. Math., 3:57-81, 2022.

(with Fukeng Huang) Implicit-explicit BDFk SAV schemes for general dissipative systems and their error analysis. Comp. Methods Appl. Math. Eng., 392:114718, 2022.

(with Xiaoli Li) Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation. Sci. China Mathematics, 65:2201-2218, 2022.

(with Qing Cheng, Pourya Delafrouz, Jie Liang and Chun Liu) Modeling and simulation of cell nuclear architecture reorganization process. J. Comput. Phys. 449:110808, 2022.

(with Sheng Chen) Log orthogonal and generalized log orthogonal functions: their approximation properties and applications to fractional differential equations. IMA J. Numer. Anal. 42:712-743, 2022.

2021

(with Xiaoli Li and Zhengguang Liu) New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis. Math. Comp. 91:141-167, 2021.

(with Yanrong Zhang) Efficient structure preserving schemes for the Klein-Gordon-Schrodinger equations. J. Sci. Comput., 89:47, 2021.

(with Beichuan Deng and Qingqu Zhuang) Second-Order SAV Schemes for the Nonlinear Schrodinger Equation and Their Error Analysis. J. Sci. Comput. 88:69, 2021.

(with Fukeng Huang) Stability and error analysis of a class of high-order IMEX schemes for Navier-stokes equations with periodic boundary conditions. SIAM J. Numer. Anal., 59:2926-2954, 2021.

(with Duo Cao and Changtao Sheng) Efficient spectral methods for PDEs with spectral fractional Laplacian. J. Sci. Comput., 88:4, 2021.

(with Xavier Antoine and Qinglin Tang) Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrodinger/Gross-Pitaevskii equations. J. Comput. Phys., 437:110328, 2021.

(with Fukeng Huang) Bound/positivity preserving and energy stable SAV schemes for dissipative systems: applications to Keller-Segel and Poisson-Nernst-Planck equations. SIAM J. Sci. Comput. 43:A1832-A1857, 2021.

(with Yiqi Gu) An Efficient Spectral Method For Elliptic PDEs In Complex Domains With Circular Embedding. SIAM J. Sci. Comput. 43:A309-A329, 2021.

(with Qing Cheng and Chun Liu) ) Generalized SAV approaches for gradient systems. J Comp. Appl. Math., 394:113532, 2021.

(With Jie Xu) Unconditionally positivity preserving and energy dissipative schemes for Poisson--Nernst--Planck equations. Numer. Math. 148:671-697, 2021.

(with Nan Zhang) Efficient and accurate SAV schemes for generalized Zakharov systems. DCDS-B 26:645-666, 2021.

(with Maojun Li, Yongping Cheng and Xiangxiong Zhang) A Bound-Preserving High Order Scheme for Variable Density Incompressible Navier-Stokes Equations. J. Comput. Phys. 425:109906, 2021.

(with Duo Cao and Jie Xu) Computing interface with quasiperiodicity. J. Comput. Phys. 424:109863, 2021.

2020

(with Xiaoli Li) On a SAV-MAC scheme for the Cahn-Hilliard-Navier-Stokes Phase Field Model and its error analysis for the corresponding Cahn-Hilliard-Stokes case. M3AS, 30:2263-2297, 2020.

(with Qing Cheng) Global constraints preserving scalar auxiliary variable schemes for gradient flows. SIAM J. Sci. Comput. 42:A2489-A2513, 2020.

(with Changtao Sheng, Tao Tang, Li-Lian Wang and Huifang Yuan) Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains. SIAM J. Numer. Anal. 58:2435-2464, 2020.

(with Fukeng Huang and Zhiguo Yang) A highly efficient and accurate new SAV approach for gradient flows. SIAM J. Sci. Comput. 42:A2514-A2536, 2020.

(with Xiaofeng Yang) The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems. Proceedings celebrating 75 years of Mathematics of Computation, Contemp. Math. 754:217-245, 2020.

(With Xiaoli Li) Error analysis of the SAV-MAC scheme for the Navier-Stokes equations. SIAM J. Numer. Anal. 58:2465-2491, 2020.

(with Qing Cheng and Chun Liu) A new Lagrange Multiplier approach for gradient flows. CMAME 367:113070, 2020.

(with Qing Cheng and Chun Liu) A new interface capturing method for Allen-Cahn type equations based on a flow dynamic approach in Lagrangian coordinates, I. One-dimensional case. J. Comp. Phys. 419:109509, 2020.

(with Yiqi Gu) Accurate and Efficient Spectral Methods for Elliptic PDEs in Complex Domains. J. Sci. Comput. 83:42, 2020.

(with Xiaoli Li) Stability and Error estimates of the SAV Fourier-spectral method for the Phase Field Crystal Equation. Adv. Comput. Math. 46:48, 2020.

(With Jie Xu) Unconditionally bound preserving and energy dissipative schemes for a class of Keller--Segel equations. SIAM J. Numer. Anal. 58:1674-1695, 2020.

(with Hongtao Chen and Jingjing Mao) Optimal error estimates for SAV finite-element schemes for gradient flows. Numer. Math. 145(1):167-196, 2020.

(with Yiqi Gu) Bound preserving and energy dissipative schemes for porous medium equation. J. Comp. Phys. 410:109378, 2020.

(with Jingwei Hu and Yingwei Wang) A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions. Kinetic and related models 13(4):677-702, 2020.

(with Sheng Chen, Zhimin Zhang and Zhi Zhou) A Spectrally Accurate Approximation to Subdiffusion Equations Using the Log Orthogonal Functions. SIAM J. Sci. Comput. 42:A849-A877, 2020.

(with Wenjuan Yao, Zhichang Guo, Jiebao Sun, and Boying Wu) A Total Fractional-Order Variation Model for Image Super-Resolution and Its SAV Algorithm. J. Sci. Comput. 82:81, 2020.

(with Feng Chen) Stability and Error Analysis of Operator Splitting Methods For American Options Under the Black-Scholes Model. J. Sci. Comput. 82:33, 2020.

(with Sheng Chen) An Efficient and Accurate Numerical Method for the Spectral Fractional Laplacian Equation. J. Sci. Comput. 82:17, 2020.

(with Jiaxiang Cai) Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. J. Comput. Phys. 401:108975, 2020.

(with Ting Cheng and Lina Ma) An efficient numerical scheme for a 3D spherical dynamo equation. J. Comp. Appl. Math., 370:112628, 2020.

(with Hongtao Chen and Jingjing Mao) Error estimate of Gauge-Uzawa methods for incompressible flows with variable density. J. Comp. Appl. Math. 364:112321, 2020.

2019

(with Feng Chen) Stability and Convergence Analysis of a Rotational Velocity Correction Method for the Navier-Stokes Equations. Adv. Comput. Math. 45:3123-3136, 2019.

(with Qingqu Zhuang) Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein Condensates. J. Comput. Phys. 396:72-88, 2019.

(with Jie Xu and Jiang Yang) A new class of efficient and robust energy stable schemes for gradient flows. SIAM Review, 61:474-506, 2019.

Efficient and accurate structure preserving schemes for complex nonlinear systems. Handbook of Numerical Analysis, V. 20: Processing, Analyzing and Learning of Images, Shapes, and Forms, Part 2, edited by R. Kimmel and X.C. Tai, 647-669, Elsevier, 2019.

(with Yingwei Wang and Jianlin Xia) Fast structured Jacobi-Jacobi transforms. Math. Comp. 88:1743-1772, 2019.

(with Changtao Sheng) Spectral methods for fractional differential equations using generalized Jacobi functions. Handbook of Fractional Calculus with Applications, V3: Numerical Methods, edited by G. Karniadakis, De Gruyter, P. 127-156, 2019.

(With Xiaoli Li and Hongxin Rui) Stability and Error Analysis of a second-order SAV scheme with Block-centered Finite Differences for Gradient Flows. Math. Comp. 88:2047-2068, 2019.

(with Ying He) Unconditionally Stable Pressure-Correction Schemes for a Non-Linear Fluid-Structure Interaction model. Comm. Appl. Math. Comp. 1:61-80, 2019.

(With Weizhu Bao, Xinran Ruan and Changtao Sheng) Fundamental Gaps of the Fractional Schrodinger Operator. Comm. Math. Sci. 17:447-471, 2019.

(with Changtao Sheng) An efficient space-time method for time fractional diffusion equation. J. Sci. Comput. 81:1088-1110, 2019.

(with Qing Cheng and Xiaofeng Yang) Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the SAV approach. J. Sci. Comput. 78:1467-1487, 2019.

(with Qingcheng Yang, Arkadz Kirshtein, Yanzhou Ji, Chun Liu, Long-Qing Chen) A Thermodynamically Consistent Phase-Field Model For Viscous Sintering. J. American Ceramic Society, 102:674-685, 2019.

2018

(with Sheng Chen) Enriched spectral methods and applications to problems with weakly singular solutions. J. Sci. Comput. 77:1468-1489, 2018.

(with Qing Cheng) Multiple scalar auxiliary variable (MSAV) approach and its application to the phase field vesicle membrane model. SIAM J. Sci. Comput. 40:A3982-A4006, 2018.

(with Jie Xu) Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. SIAM J. Numer. Anal., 56:2895,2912, 2018.

(with Changtao Sheng) A space-time spectral Petrov-Galerkin spectral method for time fractional diffusion equation. Numer. Math. Theory Methods Appl. 11 (2018), no. 4, 854-876.

(with Jing An and Zhiming Zhang) Spectral-Galerkin Approximation of a Nonlinear Eigenvalue Problem. Appl. Numer. Math., 131:1-15, 2018.

(with Haydar Alici) Highly efficient and accurate spectral approximation of the angular Mathieu equation for any parameter values q. J. Math. Study., 51:131-149, 2018.

(with Ying Chen, John Lowengrub, Cheng Wang and Steven Wise) Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. J. Comp. Phys., 365:56-73, 2018.

(with Jie Xu) Stabilized predictor-corrector schemes for gradient flows with strong anisotropic free energy. Comm. Comput. Phys. 24:635-654, 2018.

(with Sheng Chen and Li-Lian Wang) Laguerre Functions and Their Applications to Tempered Fractional Differential Equations on Infinite Intervals. J. Sci. Comput. 74 (2018), no. 3, 1286–1313.

(with Zhiping Mao) Spectral Element Method with Geometric Mesh for Two-sided Fractional Differential Equations. Adv. Comput. Math. 44:745-771, 2018.

(with Jie Xu and Pingwen Zhang) Approximations on SO(3) by Wigner D-matrix and applications. J. Sci. Comput. 74 (2018), no. 3, 1706-1724.

(with Yongyong Cai) Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field models for two-phase incompressible flows. Math. Comp. 87 (2018), no. 313, 2057-2090.

(with Zhiwei Fang and Haiwei Sun) Preconditioning techniques in Chebyshev collocation method for elliptic equations. Inter. J. Numer. Anal. Model. 15:277-287, 2018.

(with Lina Ma, Li-Lian Wang and Zhiguo Yang) Wavenumber explicit analysis of spectral-Galerkin methods for time-harmonic Maxwell equations in exterior domains. IMA J. Numer. Anal. 38 (2018), no. 2, 810–851.

(with Jie Xu and Jiang Yang) The scalar auxiliary variable (SAV) approach for gradient flows. J. Comput. Phys. 352:407-417, 2018.

2017

(with Xiaofeng Yang, Jia Zhao and Qi Wang) Numerical Approximations for a three components Cahn-Hilliard phase-field Model based on the Invariant Energy Quadratization method. Math. Models Methods Appl. Sci., 27:1993-2030, 2017.

(with Jilian Wu and Xinlong Feng) Unconditionally stable Guage-Uzawa finite element schemes for incompressible natural convection problem with variable density. J. Comp. Phys., 348:776-789, 2017.

(with Zhiping Mao) Hermite spectral methods for fractional PDEs in unbounded domains. SIAM J. Sci. Comput. 39:A1928-A1950, 2017.

(with Qing Cheng and Xiaofeng Yang) Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model. J. Comput. Phys. 341:44-60, 2017.

(with Yongyong Cai, Jie Shen and Xiang Xu) A stable scheme and its convergence analysis for a 2D dynamic Q-tensor model of nematic liquid crystals. Math. Models Methods Appl. Sci. 27 (2017), no. 8, 1459-1488.

(with Zhijian Rong and Haijun Yu) A Nodal Sparse Grid Spectral Element Method for Multi-Dimensional Elliptic Partial Differential Equations. Inter. J. Numer. Anal. Model. 14:762-783, 2017.

(with Yongyong Cai and Heejun Choi) Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. Numer. Math. 137:417-449, 2017.

(with Changtao Sheng) A hybrid spectral element method for fractional two-point boundary value problems. Numerical Mathematics: Theory, Methods and Applications. 10:437-464, 2017.

(with Haydar Alici) Highly accurate pseudospectral approximations of the prolate spheroidal wave equation for any bandwidth parameter and zonal wavenumber. J. Sci. Comput. 71:804-821, 2017.

(with Sean Colbert-Kelly, G.B. McFadden and Daniel Phillips) Numerical Analysis and Simulation for a Generalized Planar Ginzburg-Landau Equation in a Circular Geometry. Comm. Math. Sci. 15:329-357, 2017.

2016

(with Yingwei Wang) Muntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems. SIAM J. Sci. Comput., 38:A2357-A2381, 2016.

(with Zhiping Mao and Sheng Chen) Efficient and accurate spectral methods using general Jacobi functions for solving Riesz Fractional Differential Equations. Appl. Numer. Math., 106:165-181, 2016.

(with Yingwei Wang and Jianlin Xia) Fast structured direct spectral methods for differential equations with variable coefficients. SIAM J. Sci. Comput., 38:A28-A54, 2016.

(with M. Azaiez, F. Jelassi and M. Mint Brahim) Two Phases Stefan Problem with Smoothed Enthalpy. Comm. Math. Sci., 14:1625-1641, 2016.

(with Tao Tang and Jiang Yang) On the maximum principle preserving schemes for the generalized Allen-Cahn Equation. Comm. Math. Sci. 14:1517-1534, 2016.

(with Lina Hu and Lina Ma) Efficient Spectral-Galerkin Method and Analysis for Elliptic PDEs with Non-Local Boundary Conditions. J. Sci. Comput., 68:417-437, 2016.

(with Yingwei Wang and Haijun Yu) Efficient spectral-element methods for electronic Schrodinger equation in one spatial dimension. To appear in Proceedings for the Sparse Grids and Applications 2016.

(with Heejun Choi) Efficient splitting schemes for magneto-hydrodynamic equations. Science China Mathematics (English), 59:1495-1510, 2016.

(with Changtao Sheng) A hybrid spectral element method for Volterra integral equations with weakly singular kernel. Science China Mathematics (Chinese), 46:1017-1036, 2016.

(with Ying Chen) Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. J. Comput. Phys., 308:40-56, 2016.

(with Ye Cao, C. A. Randall and Longqing Chen) Effect of multi-domain structure on ionic transport, electrostatics, and current evolution in BaTiO3 ferroelectric capacitor. Acta Materialia, 1112:224-230, 2016.

(with Zhiping Mao) Efficient Spectral-Galerkin Methods for Fractional Partial Differential Equations with Variable Coefficients. J. Comput. Phys., 307:243-261, 2016.

(with Sheng Chen and Li-Lian Wang) Generalized Jacobi functions and their applications to fractional differential equations. Math. Comp. 85:1603-1638, 2016.

(with Jia Zhao, Xiaofeng Yang and Qi Wang) A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids. J. Comput. Phys. 305:539-556, 2016.

2015

(with Henk Dijkstra, Taylan Senqul and Shouhong Wang) Dynamic transitions of quasi-geostrophic channel flow. SIAM J. Appl. Math. 75:2361-2378, 2015.

(with Changtao Sheng and Zhongqing Wang) Generalized Jacobi spectral-Galerkin method for nonlinear Volterra integral equations with weakly singular kernels. J. Math. Study., 48:315-329, 2015.

(with Zhiping Mao) A semi-implicit spectral deferred correction method for two water wave models with nonlocal viscous term and numerical study of their decay rates. Science China Mathematics (in Chinese) 45:1153-1168, 2015.

(with Jing An) Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem. Comput. Math. Appl. 69:1132-1143, 2015.

(with S. Dong) A Pressure Correction Scheme for Generalized Form of Energy-Stable Open Boundary Conditions for Incompressible Flows. J. Comput. Phys. 291:254-278, 2015.

(with Xiaofeng Yang) Decoupled energy stable schemes for phase-field models of two-phase incompressible flows. SIAM J. Numer. Anal. 53:279-296, 2015.

(with Wei Li and Li-Shi Luo) Accurate solution and approximations of the linearized bgk equation for steady Couette flow. Computers & Fluids, 111:18-32, 2015.

(with Lina Ma and Lil-Lian Wang) Spectral Approximation of Time-Harmonic Maxwell Equations in Three-dimensional Exterior Domains. Inter. J. Numer. Anal. Model. 12:366-383, 2015.

(with Xiaofeng Yang and Haijun Yu) Efficient energy stable numerical schemes for a phase-field moving contact line model. J. Comput. Phys. 284:617-630, 2015.

(with Lina Hu, Claude-Michel Brauner and G.I. Sivashinsky) Modeling and Simulation of Fingering Pattern Formation In a Combustion Model. Math. Models & Methods Appl. Sci. 25:685-720, 2015.

(with Fei Liu) Stabilized Semi-Implicit Spectral Deferred Correction Methods for Allen-Cahn and Cahn-Hilliard Equations. Math. Methods Appl. Sci., 38:4564-4575, 2015.

(with Chun Liu and Xiaofeng Yang) Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density. J. Sci. Comput., 62:601-622, 2015.

(with Taylan Senqul and Shouhong Wang) Pattern Formations of 2D Rayleigh-Benard Convection with No-Slip Boundary Conditions for the Velocity at the Critical Length Scales. Math. Methods Appl. Sci. 38:3792-3806, 2015.

2014

(with Ying He and Peijun Li) A New Spectral Method for Numerical Solution of the Unbounded Rough Surface Scattering Problem. J. Comput. Phys. 275:608-625, 2014.

(with Ying He) Unconditionally Stable Pressure-Correction Schemes for a Linear Fluid-Structure Interaction Problem. Numer. Math.: Theory, Methods and Appl. 7:537-554, 2014.

(with Ye Cao, C. A. Randall and Longqing Chen) Phase-field modeling of switchable diode-like current-voltage characteristics in ferroelectric BaTiO3. Appl. Phys. Lett., DOI: 104:182905, 2014.

(with Ye Cao, C. A. Randall and Longqing Chen) Effect of ferroelectric polarization on ionic transport and resistance degradation in BaTiO3 by the phase-field approach. J. Am. Ceram. Soc., 97:3568-3575, 2014.

(with Xiaofeng Yang) Decoupled energy stable schemes for phase-field models of two-phase complex fluids. SIAM J. Sci. Comput. 36:N122-B145, 2014.

(with L. Chen, C. Xu and L. Luo) Parallel spectral-element direction splitting method for incompressible Navier-Stokes equations. Appl. Numer. Math. 84:66-79, 2014

(with Jing An) Efficient Spectral Methods for Transmission Eigenvalues and Estimation of the Index of Refraction. J. Math. Study. 1:1-20, 2014.

(with Li-Lian Wang and Haijun Yu) Approximations by Orthonormal Mapped Chebyshev Functions for Higher-Dimensional Problems In Unbounded Domains. J. Comput. Appl. Math. 265:264-275, 2014.

2013

(with Q. Wang and X. Yang) Mass and volume conservation in phase field models for binary fluids. Comm. Comput. Phys. 13:929-957, 2013

(with Jing An) A Fourier-spectral-element method for transmission eigenvalue problems in radially stratified media. J. Sci. Comput. 57:670-688, 2013.

(with Ye Cao, S. Bhattacharya, C. A. Randall and Longqing Chen) Role of polaron hopping in leakage current behavior of a SrTiO3 single crystal. J. Appl. Phys. V. 114, 224102, 2013.

(with Jing An) An Efficient and Stable Spectral-Element Method for Acoustic Scattering by an Obstacle. East Asia J. Appl. Math. 3:190-208, 2013.

(with F. Chen) A GPU Parallelized Spectral Method For Elliptic Equations. J. Comput. Phys. 250:555-564, 2013.

(with Xiaofeng Yang, Greg Forest, Huiyuan Li, Chun Liu, Qi Wang and Falai Chen) Numerical Investigation of the Dynamics of drop formation and pitch-off using a phase-field model for two-phase complex fluids. J. Comput. Phys., 236:1-14, 2013.

(with Z. Wang) Error analysis of the Strang time-splitting Laguerre-Hermite/Hermite collocation methods for The Gross-Pitaevskii equation. Foundation of Comput. Math., 13:99-137, 2013.

(with F. Chen) Efficient energy stable schemes with spectral discretization in space for anisotropic Cahn--Hilliard systems. Comm. Comput. Phys., 13:1189-1208, 2013.

(with C. Collins and S. Wise) An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Comm. Comput. Phys., 13:929-957, 2013.

2012

(with S. Dong) A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible Flows with large density ratios. J. Comput. Phys., 231:5788-5804, 2012.

(with F. Chen) Efficient spectral--Galerkin methods for systems of coupled-second-order equations and their applications. J. Comput. Phys., 231:5016-5028, 2012.

(with Peijun Li) Analysis of the Scattering by an Unbounded Rough Surface. Math. Methods Appl. Sci., 35:2166-2184, 2012.

(with Haijun Yu) On the approximation of the Fokker--Planck Equation of FENE dumbbell model, I: a new weighted formulation and an optimal spectral-Galerkin algorithm in 2-D. SIAM J. Numer. Anal. 50:1136-1161, 2012.

(with Haijun Yu) Efficient Spectral Sparse Grid Methods and Applications to High Dimensional Elliptic Problems II Unbounded domains. SIAM J. Sci. Comput. 34:A1141-A1164, 2012.

(with C. Wang, X. Wang and S. Wise) Second-order convex splitting schemes for gradient flows with Ehrlich-Schwoebel type energy: application to thin film epitaxy. SIAM J. Numer. Anal. 50:105-125, 2012.

(with F. Chen and H. Yu) A new spectral element method for pricing European options under the Black-Scholes and Merton jump diffusion model. J. Sci. Comput., 52:499-518, 2012.

(with Y. He and D. Nicholls) An efficient and stable spectral method for electromagnetic scattering from a layered periodic struture. J. Comput. Phys. 231:3007-3022, 2012.

(with L. Chen and C. Xu) A unstructured nodal spectral-element method for the Navier-Stokes equations. Comm. Comput. Phys. 12:315-336, 2012.

2011

Modeling and numerical approximation of two-phase incompressible flows by a phase-field approach. P. 147-196 in IMS Lecture Note Series, Vol 22, National University of Singapore, 2011.

(with L. Chen and C. Xu) Spectral direction splitting schemes for the incompressible Navier-Stokes equations. East Asia J. Appl. Math., 1:215-234, (2011).

(with X. Yang, G. Forest and C. Liu) Shear cell rupture of nematic liquid crystal droplets in viscous fluids. J. Non-Newtonian Fluid Mech. 166:487-499 (2011).

(with Dinesh A. Shetty, Abhilash J. Chandy and Steven Frankel) A Pressure-Correction Scheme for rotational Navier-Stokes equations and its Application to Rotating Turbulent Flows. Commun. Comput. Phys., 9:740-755 (2011).

(with L. Chen and C. Xu) A triangular spectral method for Stokes equations. Numer. Math.: Theory, Methods Appl., 4:158-179 (2011).

2010

(with Haijun Yu) Efficient Spectral Sparse Grid Methods and Applications to High Dimensional Elliptic Problems SIAM J. Sci. Comput., 32:3228-3250 (2010).

(with Li-Lian Wang) Sparse spectral approximations of high-dimensional problems based on hyperbolic cross. SIAM J. Numer. Anal., 48:1087-1109 (2010).

(with S.C. Dong) An Unconditionally Stable Rotational Velocity-Correction Scheme for Incompressible Flows. J. Comp. Phys., 229:7013-7029 (2010).

(with Xiaofeng Yang) Energy Stable Schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows. Chinese Ann. Math. series B, 31:743-758 (2010).

(with Xiaofeng Yang) A phase-field model and its numerical approximation for two-phase incompressible flows with different densities and viscosities. SIAM J. Sci. Comput., 32:1159-1179 (2010).

(with Xiaofeng Yang) Numerical Approximations of Allen-Cahn and Cahn-Hilliard Equations. DCDS, Series A, 28:1669-1691 (2010).

(with Y.Y. Kwan and J. Park) A mathematical and numerical study of incompressible flows with a surfactant monolayer. DCDS, Series A, 28:181-197 (2010).

(with Huiyuan Li) Optimal Error Estimates in Jacobi-Weighted Sobolev Spaces For Polynomial Approximations on The Triangle. Math. Comp., 79:1621-1646 (2010).

(with Qingqu Zhuang and Chuanju Xu) A coupled Legendre-Laguerre spectral-element method for the Navier-Stokes equations in unbounded domains. J. Sci. Comput., 42:1-22 (2010).

(with J. Park and F. Chen) Modeling and simulation of switchings in ferroelectric liquid crystals. DCDS, Series A, 26:1419-1440 (2010).

2009

(with Qirong Fang and Li-Lian Wang) An Efficient and Accurate Spectral Method for Acoustic Scattering in Elliptic Domains. Numerical Mathematics: Theory, Methods and Application, 2:258-274 (2009).

(with Weizhu Bao and Hailiang Li) A generalized Laguerre-Fourier-Hermite pseudospectral method for computing the dynamics of rotating in Bose-Einstein condensates. SIAM J. Sci. Comput., 31:3685-3711 (2009).

(with E. A. Eliseev, A. N. Morozovska, S. V. Kalinin, Y. Li, M. D. Glinchuk, L. Chen and V. Gopalan) Surface effect on domain wall width in ferroelectrics. J. Appl. Physics, v. 106, 084102 (2009).

(with David Nicholls) A Rigorous Numerical Analysis of the Transformed Field Expansion Method. SIAM J. Numer. Anal., 47:2708-2723 (2009).

(with Xiaofeng Yang) An efficient moving mesh spectral method for the phase-field model of twophase flows. J. Comput. Phys., 228:2978-2992 (2009).

(with Li-Lian Wang and Huiyuan Li) A triangular spectral element method using fully tensorial rational basis functions. SIAM J. Numer. Anal., 47:1619-1650 (2009).

(with Dongbin Xiu) Efficient Stochastic Galerkin Methods For Random Diffusion Equations. J. Comput. Phys., 228:266-281, 2009.

(with Li-Lian Wang) On Spectral Approximations In Elliptical Geometries Using Mathieu Functions. Math. Comp., 78:815-844, 2009.

(with Li-Lian Wang) Some Recent Advances On Spectral Methods For Unbounded Domains. Commun. Comput. Phys., 5:195-241, 2009.

(with Benyu Guo and Li-Lian Wang) Generalized Jacobi Polynomials/Functions and their Applications. Appl. Numer. Math., 59:1011-1028 (2009).

$*$ Abstract $*$ PDF file

2008

(with Weizhu Bao) A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates. J. Comput. Phys. 227:9778-9793, 2008.

$*$ Abstract $*$ PDF file

(with Mejdi Azaiez, Chuanju Xu and Qingqu Zhuang) Laguerre-Legendre spectral method for the Stokes problem in a semi-infinite channel. SIAM J. Numer. Anal., 47:271-292, 2008.

$*$ Abstract $*$ PDF file

(with Jin Ma and Yanhong Zhao) On Numerical Approximations of Forward-Backward Stochastic Differential Equations. SIAM J. Numer. Anal., 46:2636-2661, 2008.

$*$ Abstract $*$ PDF file

(with Xiaofeng Yang, Zhenlu Cui, Greg Forest and Qi Wang) Dimensional Robustness & Instability of Sheared, Semi-Dilute, Nano-Rod Dispersions. Multi. Model. Simul. 7:622-654, (2008).

$*$ Abstract $*$ PDF file

(with J.L. Guermond and Xiaofeng Yang) Error analysis of fully discrete velocity-correction methods for incompressible flows. Math. Comp. 77:1387-1405 (2008).

$*$ Abstract $*$ PDF file

(With Jiahong Wu and Yuanming Yuan) A dual-Petrov-Galerkin method for the Kawahara-type equations. J. Sci. Comput. 34:48-63, 2008.

$*$ Abstract $*$ PDF file

(with Benyu Guo) Irrational approximations and their applications to partial differential equations in exterior domains. Adv. Comput. Math. 28:237-267, 2008.

$*$ Abstract $*$ PDF file

2007

(with Chun Liu and Xiaofeng Yang) Dynamics of Defect Motion in Nematic Liquid Crystal Flow: Modeling and Numerical Simulation. Comm. Comput. Phys. 2:1184-1198, 2007.

$*$ Abstract $*$ PDF file

(with Li-Lian Wang) Analysis of a Spectral-Galerkin Approximation to the Helmholtz Equation in Exterior Domains. SIAM J. Numer. Anal., 45:1954-1978, 2007.

$*$ Abstract $*$ PDF file

(with Xiaofeng Yang) Error estimates for finite element approximations of consistent splitting schemes for incompressible flows. DCDS-B, 8:663-676, 2007.

$*$ Abstract $*$ PDF file

(with C. Zhou, P. Yue, J Feng and Chun Liu) Heart-shaped bubbles rising in anisotropic liquids. Phys. of Fluids 19, 041703 (2007).

$*$ Abstract $*$ PDF file

(With Yuen-Yick Kwan) An efficient direct parallel spectral-element solver for separable elliptic problems. J. Comput. Phys. 225:1721-1735, 2007.

$*$ Abstract $*$ PDF file

(With Jiahong Wu and Yuanming Yuan) Eventual periodicity for the KdV equation on a half-line. Phys. D. 227:105-119, 2007.

$*$ Abstract $*$ PDF file

(with Qirong Fang and D. Nicholls) A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering. J. Comput. Phys. 224:1145-1169, 2007.

$*$ Abstract $*$ PDF file

(with Li-Lian Wang) Fourierization of the Legendre-Galerkin method and a new space-time spectral method. Appl. Numer. Math. 57:710-720, 2007.

$*$ Abstract $*$ PDF file

(with Li-Lian Wang) Legendre and Chebyshev Dual-Petrov-Galerkin Methods for Hyperbolic equations. Int. J. Numer. Methods Eng. 196:3785-3797, 2007.

$*$ Abstract $*$ PDF file

(with J. Pyo) Gauge-Uzawa methods for incompressible flows with variable density. J. Comput. Phys. 221:181-197 (2007)

$*$ Abstract $*$ PDF file

(with O. Goubet) On the dual petrov-Galerkin formulation of the KDV equation on a finite interval. Adv. Diff. Eqn. 12:221-239 (2007)

$*$ Abstract $*$ PDF file

(with Dongbin Xiu) An Efficient Spectral Method for Acoustic Scattering from Rough Surfaces. Commun. in Comput. Phys., 2:54-72 (2007)

$*$ Abstract $*$ PDF file

2006

(with J. L. Guermond and P. Minev) An Overview of Projection Methods for Incompressible Flows. Comput. Methods Appl. Mech. Eng. 195:6011-6045

$*$ Abstract $*$ PDF file

(with David Nicholls) A Stable, High--Order Method for Two--Dimensional Bounded--Obstacle Scattering. SIAM J. Sci. Comput. 28:1398-1419 (2006)

$*$ Abstract $*$ PDF file

(with Leszek Demkowicz) A few new (?) facts about the infinite elements. Comput. Methods Appl. Mech. Eng. 195:3572-3590 (2006)

$*$ Abstract $*$ PDF file

(with Li-Lian Wang) Laguerre and composite Legendre-Laguerre dual-Petrov-Galerkin methods for third-order equations. DCDS-B, 6:1381-1402 (2006)

$*$ Abstract $*$ PDF file

(with R. Sani, O. Pironneau and P.M. Gresho) Pressure boundary condition for the time-dependent incompressible Navier-Stokes equations. Internat. J. Numer. Methods Fluids, 50:673-682 (2006)

$*$ Abstract $*$ PDF file

(with Xiaofeng Yang, James J. Feng, Chun Liu) Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. J. Comput. Phys., 218:417-428 (2006)

$*$ Abstract $*$ PDF file

(with Benyu Guo and Li-Lian Wang) Optimal spectral-Galerkin methods using generalized Jacobi polynomials. J. Sci. Comput. 27:305-322 (2006)

$*$ Abstract $*$ PDF file

2005

(with James J. Feng, Chun Liu, Pengtao Yue) An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. IMA Volumes in Mathematics and its Applications, 140:1--26, 2005.

$*$ Abstract $*$ PDF file

(with Li-Lian Wang) Spectral Approximation of the Helmholtz equation with high wave numbers. SIAM J. Numer. Anal., 43:623-644, 2005.

$*$ Abstract $*$ PDF file

(with Pengtao Yue, James J. Feng, Chun Liu) Transient Drop Deformation upon Startup of Shear in Viscoelastic Fluids. Phys. Fluids, 17:123101, 2005.

$*$ Abstract $*$ PDF file

(with Pengtao Yue, James J. Feng, Chun Liu) Viscoelastic effects on drop deformation in steady shear. J. Fluid Mech., 540:427-437, 2005.

$*$ Abstract $*$ PDF file

(with Weizhu Bao) A fourth-order time-splitting Laguerre-Hermite pseudo-spectral method for Bose-Einstein condensates. SIAM J. Sci. Comput., 26:2110-2028, 2005.

$*$ Abstract $*$ PDF file

(with J. L. Guermond and P. Minev) Error analysis of pressure-correction schemes for the time-dependent Stokes equations with open boundary conditions. SIAM J. Numer. Anal., 43:239-258, 2005.

$*$ Abstract $*$ PDF file

(with Pengtao Yue, James J. Feng, Chun Liu) Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 129:163-176, 2005.

$*$ Abstract $*$ PDF file

(with Pengtao Yue, James J. Feng, Chun Liu) Interfacial Forces and Marangoni Flow on a Nematic Drop Retracting in an Isotropic Fluid. J. Colloid Interface Sci., 290:281-288, 2005.

$*$ Abstract $*$ PDF file

(with Li-Lian Wang) Error Analysis For Mapped Jacobi Spectral Methods. J. Sci. Comput., 24:183-218, 2005.

$*$ Abstract $*$ PDF file

(with J.H. Pyo) Normal Mode Analysis of Second-Order Projection Methods for Incompressible Flows. Dis. Cont. Dyn. Sys. B, 5:817-840, 2005.

$*$ Abstract $*$ PDF file

(with Benyu Guo and Chenglong Xu) Generalized Laguerre approximation and its applications to exterior problems. J. Comput. Math., 23:113-130, 2005.

$*$ Abstract $*$ PDF file

2004

(with Pengtao Yue, James J. Feng, Chun Liu) A Diffuse-Interface Method for Simulating Two-Phase Flows of Complex Fluids. J. Fluid Mech. 515:293-317, 2004.

$*$ Abstract $*$ PDF file

(with J.M. Lopez and F. Marques) Complex dynamics in a short Taylor-Couette annulus with the top endwall stationary and the bottom rotating. J. Fluid Mech. 501:327-354, 2004.

$*$ Abstract $*$ PDF file

(with J. L. Guermond) On the error estimates of rotational pressure-correction projection methods. Math. Comp. 73:1719-1737, 2004.

$*$ Abstract $*$ PDF file

(with Li-Lian Wang) Error Analysis For Mapped Legendre Spectral And Pseudospectral Methods. SIAM J. Numer. Anal. 42:326-349, 2004.

$*$ Abstract $*$ PDF file

2003

(with J. L. Guermond) A New Class of Truly Consistent Splitting Schemes for Incompressible Flows. J. Comput. Phys., 192:262-276, 2003.

$*$ Abstract $*$ PDF file

A New Dual-Petrov-Galerkin Method for Third and Higher Odd-order Differential Equations: Application to the KDV Equation. SIAM J. Numer. Anal., 41:1595-1619, 2003.

$*$ Abstract $*$ PDF file

(with D. J. Seol, S. Y. Hu, Y. L. Li, L. Q. Chen and K. H. Oh) Three-dimensional phase-field modeling of spinodal decomposition in constrained films. Metals and Materials International, 9:61-66, 2003.

$*$ Abstract $*$ PDF file

(with D. J. Seol, S. Y. Hu, Y. L. Li, L. Q. Chen and K. H. Oh) Computer simulation of spinodal decomposition in constrained films. Acta Materialia, 51:5173-5185, 2003.

$*$ Abstract $*$ PDF file

(with J. L. Guermond) Velocity-correction projection methods for incompressible flows. SIAM J. Numer. Anal., 41:112-134, 2003.

$*$ Abstract $*$ PDF file

(with Chun Liu) A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Physica D. 179:211-228, 2003.

$*$ Abstract $*$ PDF file

(with Benyu Guo and Chenglong Xu) Spectral and pseudospectral approximations using Hermite functions: application to the Dirac equation. Adv. in Comp. Math., 19:35-55, 2003.

$*$ Abstract $*$ PDF file

2002

(with J.M. Lopez and F. Marques) An efficient spectral--projection method for the Navier-Stokes equations in cylindrical geometries II. Three dimensional cases, J. Comput. Phys. 176:384-401, 2002.

$*$ Abstract $*$ PDF file

(with J. Lopez and F. Marques) Mode interactions in an enclosed swirling flow: A double Hopf between azimuthal wavenumbers 0 and 2, J. Fluid Mech., 455:263-281, 2002.

$*$ Abstract $*$ PDF file

(with J.M. Lopez, J.E. Hart, F. Marques, S. Kittelman) Instability and mode interactions in a differentially-driven rotating cylinder, J. Fluid Mech., 462:383-409, 2002.

$*$ Abstract $*$ PDF file

(with Benyu Guo and Zhongqing Wang) Chebyshev Rational Spectral and Pseudospectral Methods on a Semi-Infinite Interval. Inter. J. Numer. Methods Eng. 53:65-84, 2002.

$*$ Abstract $*$ PDF file

2001

(with Benyu Guo) On Spectral Approximations Using Modified Legendre Rational Functions: Application to Korteweg-de Vries Equation on the Half Line. Indina Math. J. 50:181-204, 2001.

$*$ Abstract $*$ PDF file

(with Benyu Guo and Qiang Du) Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals, SIAM J. Numer. Anal. 39:735-762, 2001. (A Corrigendum for this paper is published in SIAM J. Numer. Anal., 41:796-798,2003)

$*$ Abstract $*$ PDF file $*$ PDF file for the Corrigendum

(with J.M. Lopez and F. Marques) A periodically forced flow displaying symmetry breaking via a three-tori gluing bifurcation and two-tori resonances, Phisica D, 156:81-97 2001.

$*$ Abstract $*$ PDF file

(with Chun Liu) On liquid crystal flows with free-slip boundary conditions, Dis. Cont. Dyn. Sys., 7:307-318, 2001.

$*$ Abstract $*$ PDF file

(with J. Zhu, L.Q. Chen and V. Tikare) Microstructure dependence of diffusional transport, Comput. Mat. Sci., v. 20, p. 37-47, 2001.

$*$ Abstract $*$ PDF file

(with J. Zhu and L.Q. Chen) Morphological evolution during phase separation and coarsening with strong inhomogeneous elasticity, Modelling Simul. Mat. Sci. Eng., v. 9, p. 499-511, 2001.

$*$ Abstract $*$ PDF file

(with J. Zhu, L.Q. Chen and V. Tikare) Computing the effective diffusivity using a spectral method, Mater. Sci. Eng. A, 311:135-141, 2001.

$*$ Abstract $*$ PDF file

2000

(with Benyu Guo and Zhongqing Wang) A rational approximation and its applications to differential equations on the half line. J. Sci. Comput. 15:117-147, 2000.

$*$ Abstract $*$ PDF file

Stable and efficient spectral methods in unbounded domains using Laguerre functions. SIAM J. Numer. Anal., 38:1113--1133, 2000.

$*$ Abstract $*$ PDF file

(with J.M. Lopez and F. Marques) Endwall effects in a periodically forced centrifugally unstable flow. Fluid Dynamics Research, vol. 27, p. 91-108, 2000.

$*$ Abstract $*$ PDF file

(with Benyu Guo) Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Numer. Math., 86:635--654, 2000.

$*$ Abstract $*$ PDF file

(with F. Wang and J. Xu) A finite element multigrid preconditioner for Chebyshev-collocation methods. Appl. Numer. Math., 33:471-477, 2000.

$*$ Abstract $*$ PDF file

A new fast Chebyshev-Fourier algorithm for Poisson-type equations in polar geometries. Appl. Numer. Math., 33:183-190, 2000.

$*$ Abstract $*$ PDF file

Before 2000

(with S. Wang and T. Tachim Mejdo) On a wind-driven, double-gyre, quasi-geostrophic ocean model: numerical simulations and structural analysis. J. Comput. Phys., 155:387--409, 1999.

$*$ Abstract $*$ PDF file

Efficient spectral-Galerkin method IV. spherical geometries. SIAM J. Sci. Comput. V. 20, 1438-1455, 1999

$*$ Abstract $*$ PDF file

(with J. Zhu, L.Q. Chen and V. Tikare) Coarsening kinetics from a variable mobility Cahn-Hilliard equation - application of semi-implicit Fourier spectral method. Phys. Review E, v. 60, No. 4, p. 3564-3572, 1999.

$*$ Abstract $*$ PDF file

(with S. Wang) A fast and accurate numerical scheme for the primitive equations of the atmosphere. SIAM J. Numer. Anal. V. 36, 719-737, 1999

$*$ Abstract $*$ PDF file

(with J.M. Lopez) Numerical simulation of incompressible flows in cylindrical geometries using a spectral projection Method, Intern. J. Appl. Sci. & Comput. V. 5, 25--40, 1998.

$*$ Abstract $*$ PDF file

(with L.Q. Chen) Applications of semi-implicit Fourier-spectral method to phase field equations. Comput. Phys. Comm. v. 108, 147-158, 1998.

$*$ Abstract $*$ PDF file

(with J.M. Lopez) An efficient spectral--projection method for the Navier-Stokes equations in cylindrical geometries I. Axisymmetric cases, J. Comput. Phys. v. 139, p. 308-326, 1998

$*$ Abstract $*$ $*$ PDF file

Efficient spectral-Galerkin method III. polar and cylindrical geometries, SIAM J. Sci. Comput. Vol. 18, 1583-1604, 1997

$*$ Abstract $*$ PDF file

(with R. Temam) Nonlinear Galerkin method using Legendre polynomials, in ``Studies in Advanced Mathematics'', vol. 3, 363--376, AMS and International Press, 1997.

$*$ Abstract $*$ PDF file

Pseudo-compressibility methods for the unsteady incompressible Navier-Stokes equations, in "Proceedings of the 1994 Beijing Symposium on Nonlinear Evolution Equations and Infinite Dynamical Systems", 68--78, Ed. Boling Guo, ZhongShan University Press, 1997.

$*$ Abstract $*$ PDF file

On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes, Math. Comp. vol. 65, 1039--1065, 1996.

$*$ Abstract $*$ PDF file

(with W.B. Liu) A new efficient spectral Galerkin method for singular perturbation problems, J. Sci. Comput. vol. 11, 411--437, 1996.

$*$ Abstract $*$ PDF file

Effcient Chebyshev-Legendre Galerkin methods for elliptic problems, Proceedings of ICOSAHOM'95, p. 233-239, Houston J. Math. 1996.

$*$ Abstract $*$ PDF file

On a new pseudo-compressibility method for the incompressible Navier-Stokes equations, Appl. Numer. Math. vol. 21, 71-90, 1996.

$*$ Abstract $*$ PDF file

On error estimates of the penalty method for the unsteady Navier-Stokes equations, SIAM J. Numer. Anal. Vol. 32, 386-403, 1995.

$*$ Abstract $*$ PDF file

(with R. Temam) Nonlinear Galerkin methods using Chebyshev and Legendre polynomials I. one dimensional case, SIAM J. Numer. Anal. Vol. 32, 215-234 (1995).

$*$ Abstract $*$ PDF file

On fast direct poisson solver, inf-sup constant and iterative Stokes solver by Legendre Galerkin method, J. Comput. Phys. Vol. 116, 184-188 (1995).

$*$ Abstract $*$ PDF file

Efficient spectral-Galerkin method II. Direct solvers for second- and fourth-order equations using Chebyshev polynomials, SIAM J. Sci. Comput. vol. 16, 74-87 (1995).

$*$ Abstract $*$ PDF file

Efficient spectral-Galerkin method I. Direct solvers for second- and fourth-order equations using Legendre polynomials, SIAM J. Sci. Comput. vol. 15, 1489-1505 (1994).

$*$ Abstract $*$ PDF file

Remarks on pressure error estimates of the projection methods, Numer. Math. vol. 67, 513-520 (1994).

$*$ Abstract $*$ PDF file

A remark on the projection-3 method, Intern. J. Numer. Methods Fluids, 16, 249-253 (1993).

$*$ Abstract $*$ PDF file

On pressure stabilization method and projection methods for unsteady Navier-Stokes equations, Advances in Computer Methods for Partial Differential Equations-VII (eds. R. Vichnevestsky, D. Knight and G. Richter), 658-662, IMACS 1992.

$*$ Abstract $*$ PDF file

On error estimates of some higher-order projection and penalty-projection methods for the Navier-Stokes equations, Numer. Math., Vol. 62, 49-73 (1992).

$*$ Abstract $*$ PDF file

On error estimates of the projection methods for the Navier-Stokes equations: first-order schemes, SIAM J. Numer. Anal., Vol. 29, 55-77 (1992).

$*$ Abstract $*$ PDF file

Projection schemes for the Navier-Stokes equations. Appl. Math. Let., 5:35--37, 1992.

Hopf bifurcation of the unsteady regularized driven cavity flow, J. Comp. Phys. Vol. 95, 228-245 (1991).

$*$ Abstract $*$ PDF file

On an unconditionally stable scheme for the unsteady Navier-Stokes equations., J. Comput. Math., 8(3):276--288 (1990).

$*$ Abstract $*$ PDF file

Long time stability and convergence for fully discrete nonlinear Galerkin methods, Appl. Anal., 38, 201-229 (1990).

$*$ Abstract $*$ PDF file

(with B. Michaux and J.M. Rakotoson) On the approximation of a quasilinear equation. Math. Model. Numer. Anal., 24(2):211--234, 1990.

Convergence of approximate attractors for a fully discrete system for reaction-diffusion equations, Numer. Func. Anal. Optim., 10, 1213-1234 (1989).

$*$ Abstract $*$ PDF file

Dynamics of regularized cavity flow at high Reynolds numbers. Appl. Math. Lett., 2(4):381--384, 1989.

(with R. Temam) A new fractional scheme for the approximation of incompressible flows. Mat. Aplic. Comput., 8(1):3--22, 1989.

(with B. Michaux and J.M. Rakotoson) On the existence and regularity of solutions of a quasilinear mixed equation of Leray-Lions type. Acta Appl. Math., 12:287--316, 1988.

A spectral-tau approximation for the Stokes and Navier-Stokes equations, Math. Model. Num. Anal. 22:677-693 (1988).

$*$ Abstract $*$ PDF file