Exercise Sheets

I. Introduction

1. Classification, Transformation of Variables (pdf)

II. Elliptic Equations

2. Finite Differences, Laplace Operator (pdf)
3. Sobolev Spaces and Weak Derivatives (pdf)
4. Weak Solutions and Ritz-Galerkin Method (pdf)

III. Parabolic Equations

5. title (pdf)
6. title (pdf)
7. title (pdf)

IV. Hyperbolic Equations of Second Order

8. (pdf)
9. (pdf)

V. Hyperbolic Systems of First Order

10. title (pdf)

VI.

11. title(pdf)
12. title (pdf)

VII.

13. title (pdf)

Information Resources for Matlab and Scilab

Matlab PDE Toolbox

The Partial Differential Equation Toolbox

Eine sehr kurze Einführung in die Partial Differential Equation Toolbox von Matlab

Using the Matlab PDE toolbox

The PDE Toolbox - Minicourse

Finite Elemente

Das kleine Finite-Elemente-Skript, VL-Skript von A. Jüngel, 2004.

Finite Elemente in Scilab: Das Lösen partieller Differentialgleichungen mit Hilfe der FreeFEM-Toolbox

FreeFEM for Scilab / SciFreeFEM

Openfem_scilab

OpenFEM (An Opensource Finite Element Toolbox)

CALFEM (Computer Aided Learning of the Finite Element Method)

Korrekturen zum Buch von Braess

Mehrgitterverfahren

MGNet - Homepage

Multigrid Workbench (self-guided tour through multigrid algorithms)

An Introduction to Multigrid Methods (Online-Buch von Pieter Wessling)

MGLab (interactive environment for experimenting with multigrid algorithms, MATLAB)

A short paper describing MGLab

MUDPACK multigrid software package (fortran)

• Lloyd N. Trefethen, Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, unpublished text, 1996, (now available online).
• Some disasters attributable to bad numerical computing (Douglas N.Arnold)
• PDELab: Problem Solving Environment for PDE Applications (Purdue University)
• NumaWWW : Numerical Mathematics in the WorldWideWeb (TU Darmstadt):
• Partial Differential Equations