Math 621 - Numerical Analysis II

Numerical Methods for Partial Differential Equations

Fall 2007 - Matthias K. Gobbert

Detailed Schedule - Last Updated October 25, 2007


This schedule is designed to give you an overview of the material to be covered and is tentative in nature. This is a living document and will be updated throughout the semester.
The entries in the column References point to a number of standard references in the field. See my webpage on recommended literature for the complete citations.
Class Date Main Topic References
1 We 08/29 Overview: an application example Gobbert (SISC)
Mo 09/03 Labor Day
2, #1 We 09/05 Prototype problems for elliptic, parabolic, and hyperbolic PDEs Evans (Ch. 1 and 2)
3 Mo 09/10 The finite difference method for elliptic problems Gobbert (Notes)
4 We 09/12 Linear solvers and Matlab programming
5 Mo 09/17 Idea of the finite element method for elliptic problems Gockenbach
We 09/19 12:00-01:00, ENGR 122: CIRC Workshop: Advanced Programming in MATLAB CIRC Tutorial
6 We 09/19 Weak derivatives and Sobolev spaces Braess (Sec. II.1)
7, #2 Mo 09/24 The weak form of elliptic PDEs Braess (Sec. II.2)
8 We 09/26 Galerkin orthogonality and Céa's lemma, standard finite elements Braess (Sec. II.4, II.5)
Fr 09/28 02:30-03:30, MP 401: Colloquium talk: methods for non-linear reaction-diffusion equations
9 Mo 10/01 Approximation theory and convergence of the FEM in the H1- and L2-norms Braess (Sec. II.6-II.7)
10, #3 We 10/03 Introduction to COMSOL Multiphysics: GUI and scripting Gobbert (COMSOL)
11 Mo 10/08 Test (FD and FEM for elliptic problems)
12 We 10/10 Demonstration of the CAD facilities of COMSOL Multiphysics
13 Mo 10/15 Analysis of FEM convergence in COMSOL Multiphysics Gobbert (COMSOL)
14, #4 We 10/17 The method of lines for a parabolic prototype problems using FD Yang & Gobbert (Tech. Rep.)
15 Mo 10/22 Review of basic numerical methods for ODEs and their convergence theory Ascher & Petzold
16, #5 We 10/24 Linear stability theory for ODE methods and the concept of stiffness Ascher & Petzold
17 Mo 10/29 Numerical methods for stiff systems of ODEs Shampine & Reichelt
18 We 10/31 The non-linear solver inside implicit ODE methods Gobbert et al. (SISC)
19, #6 Mo 11/05 Implementation issues and higher dimensional problems Gobbert et al. (SISC)
20 We 11/07 The finite element method for parabolic problems Gobbert (SISC)
21 Mo 11/12 Theory of the finite element method for parabolic problems Thomée (Ch. 1)
22 We 11/14 Parallel computing for non-linear reaction-diffusion equations Gobbert (SISC)
23, #7 Mo 11/19 Theory of hyperbolic partial differential equations Strikwerda (Sec. 1.1-1.2)
24 We 11/21 Finite differences for the scalar transport equation Strikwerda (Sec. 1.3-1.4)
25 Mo 11/26 Theory for FD for the scalar transport equation Strikwerda (Sec. 1.5-1.6)
26 We 11/28 Finite elements for hyperbolic conservation laws Baumann & Oden
27, #8 Mo 12/03 Parallel computing for hyperbolic conservation laws Gobbert et al. (JSC)
28 We 12/05 Other numerical methods for PDEs and review
29 Mo 12/10 Preparation for project presentations
Fr 12/14 02:30 p.m. Project Presentations Note date and time!

Copyright © 1999-2007 by Matthias K. Gobbert. All Rights Reserved.
This page version 2.0, October 2007.