Numerical Methods for PDEs

Lecturer

Dr. Jaroslav Vondřejc,

Varun Bharadwaj

Please register via StudIP

Numerische Methoden für PDEs

j.vondrejc@tu-bs.de

Lecture: Wed 09:45-11:15 o'clock in room PK 3.4. (Pockelsstraße 3, Am Okerufer, Hochhaus, 205)

Tutorials: Friday 13:15-14:45 o'clock in our institute at Mühlenpfordtstrasse 23, 8 floor; there will be an extra tutorial (because of the canceled one) scheduled on Friday 23/6 at 11:30 in our institute.

Wednesday 5.4.2016

Introduction to PDEs and Numerical Methods

INF-WR

j.vondrejc@tu-bs.de

here

here

• Braess, D. (2007). Finite elements: Theory, fast solvers, and applications in solid mechanics. Cambridge University Press.
• Gockenbach, M. S. (2010). Partial differential equations: analytical and numerical methods. 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.).

• Lecture 1: Basis informations, motivation.
• Lecture 2-3 (section 2): Lebesgue spaces, some inequalities, completeness
• Lecture 4: Sobolev spaces, Hilbert spaces, Banach spaces
• Lecture 5: Variational problems
• Lecture 6: Discretisation of variational problems
• Lecture 7: FEM, influence of numerical integration
• Lecture 8-9: (sections 8-10): Saddle-point problems - discrete formulations
• Lecture 10-11: Adaptive methods

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

• Assignment 1 (Norms, inequalities, closure, completeness), deadline 26/4/2017, solution
• Assignment 2 (Sobolev norms and weak formulations using FEniCS), deadline Friday 12/5 before tutorial (changed)
• Reading assignmen R1: D. Braess (2007). Finite elements: Theory, fast solvers, and applications in solid mechanics. Chapter III, paragraphs 1, 2, and 3. Solution theory can be found here and python code in bitbucket repository.
• Assignmen 3 (Assembling of FEM matrices, propreties of FEM linear systems), deadline Friday 19/5 before tutorial. The solution is partly in repository partly explained in pdf.
• Assignment 4 (convergence of FEM, basic properties of saddle-point linear systems), deadilne before lecture on Wednesday 14/6/2017. New Hints were added.
• Voluntary assignment 5 (the points does not count): Solve assignment 1 in third block from last year. Python script can be found in bitbucket repository.
• Reading assingment: D. Braess (2007). Finite elements: Theory, fast solvers, and applications in solid mechanics. Chapter III, paragraph 4.
• Assignment 6 (Mixed formulation, RT elements). Deadline Wednesday 12/7 before lecture.
• Reading assignment: Chapters 6,14-15 in Gockenbach: Understanding and Implementing the FEM