Course archive
Numerical Methods for Partial Differential Equations
Archived course information for the summer term 2020.
Archived course page: The information below refers to the summer term 2020.
Overview
- Lecturer: Raphael Kruse
- Teaching assistant: Rico Weiske
- Format: 4 hours of lectures and 2 hours of tutorials per week
- Language: German / English
- Suitable, among others, for modules: MAT.05312, MAT.05315, MAT.05320, MAT.05323, MAT.05325, MAT.05382
The course was delivered online. Materials and further information were provided via Stud.IP.
Topics
- Typical differential equations of mathematical physics
- Classification of partial differential equations: elliptic, parabolic and hyperbolic
- Classical solution methods, including separation of variables and characteristics
- Finite differences for elliptic differential equations: consistency, stability, convergence and maximum principles
- Finite differences for first-order partial differential equations and transport equations
- Variational formulations of elliptic boundary-value problems, weak derivatives, Sobolev spaces and the Lax–Milgram theorem
- Galerkin methods and their convergence
- Finite element methods for elliptic boundary-value problems: implementation and error analysis
- Iterative solvers for large sparse linear systems
Programming exercises
Programming assignments formed an essential part of the tutorials. Submission and review were organised using the Institute’s Git server.