MATH 817     Introduction to Numerical Methods for Partial Differential Equations

Fall 2010



Basic information

Calendar (updated every week)

Progr means that the corresponding lecture is about algorithmic development and programming.

Week Lecture   Description
Section
in book
HW&Q                                    
1 09/01 W                                                   
  Quiz #0 (not graded)                
2 Labor day
09/08 W Maximum pple for 2-point BVP 
 2.1  
3 09/13 M FD for 2-point BVP
Progr
 
09/15 W FD for 2-point BVP
4.1 Quiz #1 [Sect 2.1]
4 09/20 M FD for 2-point BVP 4.1
 
09/22 W FD for the Poisson equation Progr HW #1 due
5 09/27 M Maximum pple for elliptic BVP 3.1-3.2   
09/29 W FD for the Poisson equation 4.2 Quiz #2 [Sect 4.1 & 3.2] 
6 10/04 M Sobolev spaces
Appendix
 
10/06 W Variational formulation for a 2-point BVP 2.3 HW #2 due
7 10/11 M Finite element methods for a 2-point BVP 5.1  
10/13 W Programming the FEM
Progr Quiz #3 [Sect 2.3 & Appendix]
8 10/18 M Programming the FEM
Progr  
10/20 W Elliptic problems in the plane
3.5, 3.6 & 5.2

9 10/25 M Theory of FEM in 1 dimension
5.1
HW #3 due
10/27 W Theory of FEM in 2 dimensions
5.3 & 5.4
Project #1 due
10 11/01 M Parabolic problems
8.2 & 8.4
 
11/03 W Explicit FD for the heat equation
9.2
Quiz #4 [3.5, 3.6, 5.1, 5.2, 5.3 & 5.4] - Long Quiz: 30 min.
11 11/08 M Implicit FD for the heat equation
9.2
 
11/10 W L^2 analysis of the CN method
9.2

12 11/15 M Semidiscretization in space for parabolic problems
9.3
HW #4
11/17 W FEM for parabolic problems
9.3

13 11/22 M FEM for the wave equation
Progr
Quiz #5 [9.2 - take home]
Thanksgiving vacation
14 11/29 M FEM for the wave equation Progr
HW #5 due
12/01 W FEM for the wave equation Progr
Project #2 due
15 12/06 M
 
12/08 W    

Auxiliary materials (UPDATED 09/22)

Notes document. This document will be growing for a while. Be considerate and thrifty: Do not print everything, every time! So far, the file contains:
  1. Proofs of Section 2.1 [Maximum principle for 2-point BVP]
  2. Proofs of Section 4.1 [Finite difference method for 2-point BVP]

Matlab tips and code for this class

  1. MATLAB Tips & Examples. (UPDATED 10/20).
  2. Programs for lecture #3 (09/13) : finite difference code + scripts for testing
  3. Programs for lecture #6 (09/22) : fd for Poisson + scripts for testing
  4. A two dimensional P1-FEM code. Instructions and documentation  Serious update on 10/20 
  5. Programs for lecture #13 (10/18) : prepare grid + expand grid + FEM matrices 
  6. Programs for lecture #14 (10/20) : P1-FEM code + routine to compute errors + scripts 
  7. Programs for lecture #20 (11/10) : Implicit Euler for the heat eqn + scripts
  8. Programs for lecture #23 (11/22) : FEMprepare2wave + loadplustraction (modified version of loadplustraction 11/29)
  9. Programs for lecture #24 (11/29) : NewmarkFEM

Quizzes and Homework (UPDATED 11/22)

  1. Quizzes #1, #2, #3 & #4 with solutions. Click here
  2. Homework Assignments #1, #2, #3, #4 & #5 and Project #1. Click here