Math 621 - Numerical Analysis II

Numerical Methods for
Partial Differential Equations

Fall 2003 - Matthias K. Gobbert

Detailed Schedule - Last Updated November 13, 2003

This schedule is designed to cover the material in a slightly accelerated lecture schedule by lengthening each class by 15 minutes. The goal is to allow the projects at the end of the semester to use also material that is only covered towards the end of the lectures. Please let me know if any of this is unclear.
This schedule is designed to give you an overview of the material to be covered and is tentative in nature.
The chapter numbers refer to the text, Arieh Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 1996. Additional material, in particular on the theory of the finite element method, will be taken from Braess (2001) and Thomée (1997).
Class Date Main Topic Chapter
1 We 08/27 Overview of prototype problems for the semester
Reading: Chapter 1, Appendix A, and parts of Chapter 2 of Evans
Mo 09/01 Labor Day
2, #1 We 09/03 Evans: Theory of partial differential equations
Reading: Chapters 1, 8, and Appendix A of Notes
3 Mo 09/08 Examples of partial differential equations in applications
Reading: Chapter 2 of Notes
4 We 09/10 The finite difference method for elliptic problems 7
5, #2 Mo 09/15 Theory of the finite difference method for elliptic problems 13
Reading: Chapter 3 of Notes
6 We 09/17 The finite difference method for parabolic problems 13
7 Mo 09/22 Stiff ODEs and review of numerical methods for ODEs 4
8 We 09/24 Newton method for non-linear parabolic problems
9, #3 Mo 09/29 Test 1 (finite difference methods)
10 We 10/01 Introduction to the finite element method for elliptic problems
Reading: Paragraphs II.1 and II.2 of Braess
11 Mo 10/06 Sobolev spaces and their norms
Reading: Paragraph II.4 of Braess
12 We 10/08 The weak formulation and unique existence of solutions
Reading: Paragraphs II.6 and II.7 of Braess
13 Mo 10/13 Approximation error of finite element and convergence theorem
Reading: FEMLAB User's Guide and Introduction
14 We 10/15 Introduction to FEMLAB
15, #4 Mo 10/20 Approximation error of finite element and convergence theorem
Reading: Chapter 1 of Thomée
16 We 10/22 The finite element method for parabolic problems
17 Mo 10/27 Theory of the finite element method for parabolic problems
Reading: Chapter 1 of Strikwerda
18 We 10/29 Finite differences for the scalar transport equation 14
Mo 11/03 No class
19, #5 We 11/05 Test 2 (finite element methods)
20 Mo 11/10 Examples of Partial Differential Equations in Applications
21, #6 We 11/12 Implementation issues of finite element methods
Reading: Paper by Baumann and Oden
22 Mo 11/17 Finite elements for hyperbolic conservation laws
23 Mo 11/24 Project Presentations
24 We 11/26 Project Presentations
25 Mo 12/01 Review
Copyright © 1999-2003 by Matthias K. Gobbert. All Rights Reserved.
This page version 5.5, November 2003.