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466716-FS2023-0-Numerical Methods for Partial Differential Equations





Root number 466716
Semester FS2023
Type of course Lecture
Allocation to subject Mathematics
Type of exam not defined
Title Numerical Methods for Partial Differential Equations
Description Part I: Weak solutions of elliptic problems
1. Problems with non-classical solutions, motivation of the weak formulation.
2. Weak derivatives.
3. Sobolev spaces, traces, Poincaré-Friedrich inequalities.
4. Weak formulations of the Dirichlet and Neumann problem for the Laplace operator.
5. Lax-Milgram theorem

Part II: Finite element methods
6. Galerkin approach, Céa's lemma
7. Construction of FEM spaces
8. Bramble-Hilbert approximation lemma
9. Error estimates and convergence

Part III: Implementation in Matlab

Part IV: A posteriori error estimates
10. Elliptic reconstruction
11. Residual-based estimates
12. Mesh refinements
13. Convergence
14. Computational implementation

Pari V: Evolution problems
15. Theta scheme
16. Full discretization
17. CFL condition
ILIAS-Link (Learning resource for course) Registrations are transmitted from CTS to (no admission in ILIAS possible). ILIAS
Link to another web site
Lecturers Prof. Dr. Thomas Wihler, Institute of Mathematics ✉
ECTS 6
Recognition as optional course possible Yes
Grading 1 to 6
 
Dates Monday 13:15-16:00 Weekly
Tuesday 13:15-14:00 Weekly
 
Rooms Hörsaal B007, Exakte Wissenschaften, ExWi
Hörraum B078, Exakte Wissenschaften, ExWi
 
Students please consult the detailed view for complete information on dates, rooms and planned podcasts.