Numerical Methods for PDEs

General Information

Lecturer

Dr. Anna Veselovska

Please register via StudIP

Numerische Methoden für PDEs

j.vondrejc@tu-bs.de

Lecture: Wed 09:55-11:25 o'clock in the seminar room of the Institute of Scientific Computing, Mühlenpfordstrasse 23.

Tutorials: Friday 13:15-14:45 in the seminar or computer room of the Institute of Scientific Computing, Mühlenpfordstrasse 23.

Wednesday 10.4.2019

Introduction to PDEs and Numerical Methods

INF-WR

j.vondrejc@tu-bs.de

here

Braess, D. (2007). Finite elements: Theory, fast solvers, and applications in solid mechanics. Cambridge University Press.
Gockenbach, M. S. (2006). Understanding and implementing the finite element method. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics.
Langtangen, H.P., Logg, A.: Solving PDEs in Python: The FEniCS Tutorial I, Springer.
Bitbucket repository contains some python scripts. See also repository with codes for PDE1.
Hints for FEniCS and Python (Installation, tutorials, etc.) - it will be updated at the beginning of the semester.

Lecture 1: Organisation of the course, motivation, examples on Bitbucket repository.
Lecture 3: Finite element method in 2D and 3D, numerical integration.
Lecture 2: Lebesgue spaces, norms, scalar product.
Lecture 3-4: Sobolev spaces.
Lecture 5: Existence of a solution to PDEs
Lecture 6: Discretisation of PDEs
Lecture 7: Convergence of FEM
Lecture 8-12: Saddle point problems.

In case you find some bugs or typos in the lectures, please contact Jaroslav on email or edit the source on Overleaf.

Please, submit electronic document (e.g. code) to email address: wire.pde(at)gmail.com

The assignments are published on StudIP.
Reading assignment: Chapter II, paragraph 1 (Sobolev Spaces) in the book of Braess (2007). Deadline Wednesday 5.6. before lecture.
Reading assignment: Saddle point problems in the book of Braess (2007). Chapter III, paragraphs 4 and 5.