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0366-4185.01 Numerical Methods for Partial Differential Equations (Boundary Value Problems)

Spring Semester 2010
Graduate Course

BOOKS

Finite Elements

An Analysis of the Finite Element Method by Strang and Fix

Numerical Solution of Partial Differential Equations by the Finite Element Method
by Claes Johnson

The Mathematical Theory of Finite Element Methods (2nd edition)
by Brenner and Scott

Finite Element Method Analysis by Szabo and Babuska

Finite Elements: An Introduction Vol 1 by Becker, Carey and Oden

Computational Galerkin Methods by Fletcher

Introduction to Finite and Spectral Elelement Methods using MATLAB by C. Pozrikidis

Finite Difference Schemes and Partial Differential Equations by J.C. Strikwerda

Multigrid & CG

A Multigrid Tutorial second edition
by W.L. Briggs, V.E. Henson and S.F. McCormick

Iterative Methods for Sparse Linear Systems (second edition)
by Yousef Saad

Multigrid by U. Trottenberg, C.W. Oosterlee and A. Schuller

An Introduction to Multigrid Methods by P. Wesseling

Multigrid Methods by J. H. Bramble, James H. Bramble

Iterative Methods for Solving Linear Systems by Anne Greenbaum

Iterative Solution Methods by Owe Axelsson

General

Finite Difference Schemes and Partial Differential Equations (second edition)
by John Strikwerda

Numerical Mathematics by Quarteroni, Sacco and Saleri

Numerical Partial Differential Equations by J.W. Thomas

Partial Differential Equations for Computational Science by David Betounes

Some links are
MATLAB PDE toolbox
mgnet
netlib
www.engr.usask.ca
http://www.dealii.org finite element library C++
www.mcs.dundee.ac.uk
www.featflow.de
Felt.sourceforge.net
MATLAB routines

Time and Place:
Sunday 10:00-13:00 Shreiber, room 209.


Course outline

This list will be updated as the course progresses.
  1. Finite Differences
  2. Finite Elements
    - Sobolev spaces
    - weak formulation
    - variational formulation
    - essential and natural boundary conditions
    - 2D elements
  3. Multigrid
  4. Conjugate Gradient
  5. Parabolic Equations
  • Strang demo FEM code
  • FEM meshing
    • The grade will be given based on a final project due the week after succot. For details of the final project see Final Project
    The final project is due no later than sunday September 16, 2007
    It can be done in pairs (add a little).