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Numerical solution of differential equations
Numerik der Differentialgleichungen
Last Updated: 2026-02-05 15:00:08
Abstract
Methods for the numerical solution of partial differential equations of elliptic, parabolic and hyperbolictype. Finite Element, Finite Difference and Finite Volume Methods. A-priori and a-posteriorierror estimation. MATLAB implementation in one and two spatial dimensions.
Objective
Uebersicht ueber die wichtigsten Methoden zur Numerischen Loesung partieller Differentialgleichungen, insbesondere elliptischer, parabolischer sowie hyperbolischer linearer Differentialgleichungen. Uebersicht ueber Theorie plus Implementierung der Methoden.
Content
Elliptic problems. Diffusion. Finite Element Methods, Finite Difference Methods: analysis and implementation. Direct and iterative solution of linear systems of equations. A-priori and a-posteriori error estimation. Adaptive Mesh Refinement Algorithms in 1-d and in 2-d. Indefinite Problems of Helmholtz type. Problems with constraints. Stokes Problem. Inf-sup Condition and divergence stable Finite Elements. Eigenvalue problems and their FE discretization. Linear parabolic problems. Explicit and implicit timestepping schemes. Finite Difference Methods for linear and nonlinear hyperbolic problems in one space dimension.
Resources
Lecture Notes
Skript is provided.
Literature
D. Braess, Finite Elements, Cambridge Univ. Press
General Information
- Language
- German
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 180 minutes
- Aids
- 10 DIN A4 Blätter beidseitig beschrieben, Taschenrechner.
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Numerik der Differentialgleichungen |
|
4 h weekly |
| exercise | Numerik der Differentialgleichungen |
|
2 h weekly |