Numerik für Differentialgleichungen

Prof. Dr. Dominik Göddeke

Vorlesung
tba, in particular online vs. on-site

Erste Vorlesung:
tba

Übung
tba

We discuss variations of Finite Element discretization schemes
for diffusion-dominated PDEs, including the time-dependent case, and associated solver aspects. This includes the well-posedness theory, discretization errors, adaptive schemes, but also implementational aspects.

A tentative list of topics is:

•  Coercivity and inf-sup stability,
   Galerkin and Petrov-Galerkin projections
• Matching Finite Element methods
  and their a priori error estimates
  
  
• Multigrid methods to solve the resulting
  linear equations optimally
  
  
• Extension to the time-dependent case
  by Discontinous Galerkin methods
  
  
• Adaptive methods

We assume basic knowledge of the weak solution theory for PDEs, exemplarily for the Poisson problem.
However, the lecture is self-contained and can be followed based on knowledge from Numerics I.
For the practical part of the exercises, Python is recommended, on the level of Numerics I.

Bemerkungen:
This 9LP lecture also exists in a 6LP version, for the M.Sc. SimTech degree programme. This will be implemented as usual, i.e., attending until Christmas or attending all the time and doing the exam only on the material presented until Christmas.

See Ilias

M.Sc. Mathematik, M.Sc. SimTech

9 LP (or 6)

oral exam