Zhiqiang Cai's Math/CS 615 Class

MA 61500  TTh 1:30pm--2:45, SCHM 123

Numerical Methods for Partial Differential Equations

Professor Zhiqiang Cai
OFFICE: Math 412
OFFICE PHONE: (765)494-1921
OFFICE HOURS: Tuesday and Thursday 12-1pm
E-MAIL: caiz@purdue.edu
URL: http://www.math.purdue.edu/~caiz

GRADER: Junpyo Choi
Grader's OFFICE: MATH 707
Grader's office hour:
Grader's E-MAIL: choi508@purdue.edu



TEXTBOOK:

References



LECTURE NOTES (Spring 2025)

Chapter 1a. Piecewise Polynomials and Approximation Theory

Chapter 1b. Piecewise Polynomials and Approximation Theory

Code for 1d Least-squares approximation

Chapter 1c. Efficient Shallow Ritz Method

Chapter 1d. Piecewise Polynomials and Approximation Theory

Chapter 2a. PDEs and their Equivalent Formulations

LECTURE NOTES (Spring 2023)

Outline

PDEs and their Equivalent Formulations

Classes of Approximating Functions

Numerical Methods

Homework Problems

Solution of Homework Problems 1



LECTURE NOTES (Sringe 2021)

Basic Comcepts (2021)

Sobolev Space (2021)

Variational Formulation (2021)

Finite Element Space (2021)

Approximation Theory (2021)

n-Dimensional Variational Problems

Talk Slides on AFEM



Matlab FEM Codes

50 Lines of Matlab for FEM

FEM Code with Matlab II

Long Chen's Matlab Code for Adaptive FEM