Wintersemester 2021/22

Introduction to the Numerics of Partial Differential Equations

Vorlesung

Dozent
Zeit und Ort

Vorlesung
Dienstag , 14:00 - 15:30 vom 26.10.2021 bis 08.02.2022 
PWR 57 - 7.122 (PF57/07/7.122)

Donnerstag , 09:45 - 11:15 vom 21.10.2021 bis 10.02.2022 
PWR 57 - 7.122 (PF57/07/7.122)

Erste Vorlesung:
Dienstag, 26.10.2021

Übung
Donnerstag , 11:30 - 13:00 von 21.10.2021 bis 10.02.2022 
PWR 57 - 7.122 (PF57/07/7.122)

 
Inhalt

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
Vorkenntnisse

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.

Literatur

See Ilias

Curricula

M.Sc. Mathematik, M.Sc. SimTech

Leistungspunkte

9 LP (or 6)

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