Seminar
Numerical Methods for Flow Problems

Tutors:	Daniel Arndt, Dörte Jando
Class data:	LSF
Seminar:	Mon 14-16h, Mathematikon (INF 205), Seminarraum 11, Start: April 24, 2017

Summary

The simulation of flow problems is of great importance in many applications, for example in the design process of new aircrafts or cars and simulations of air flow in the interior of buildings. Therefore, the analysis of numerical simulation methods is an important research field. Flow problems are often characterized by sattle point structures resulting from divergence constraints, by instationary phenomena and/or instabilities resulting from advection dominance. In this seminar we treat numerical methods to solve such problems using finite element methods.

Target group

Students of mathematics (BSc and MSc) as well as students of scientific computing (MSc).

Prior knowledge

Numerics for PDEs. Optionally: Numerical analysis of ordinary differential equations.

Participation

For participation in the seminar you have to register via Müsli (binding registration).

Additionally, please write us a mail with your subject of study, semester, BSc / MSc, ... . Please also mention related lectures you have already attended, courses you will take in the summer term. Generally, the seminar topic could already serve as preparation phase for your thesis.

Preparation

The topics will be assigned starting from now. Interested students can prepare their presentations already in the semester break (we do recommend that). Latest assignment is in the beginning of the summer term. Generally, before presenting we recommend to discuss the structure of your talk with us.

Topics

The seminar covers the following topics:

1. Sattle point problems in an abstract setting (inf sup stability, Stokes, suitable finite elements), literature
2. IMEX for diffusion-advection problems?
3. Splitting methods for time integration of flow problems (Guermond)
4. Advection-diffusion problems and SUPG (Roos, Stynes, Tobiska)
5. A posteriori error estimation for diffusion-dominant problems
6. A posteriori error estimates for stabilized finite element methods (Tobiska, Verfuerth)

You are most invited to propose additional topics that fit into the area.

Schedule

Date	Participant	Topic
12.06.2017	Saurabh Mehta	Projection-based Time Discretization
19.06.2017
26.06.2017	Jonathan Schwegler	Streamline Diffusion Finite Element Method
03.07.2017	Santiago Ospina De Los Ríos	Locally Stabilized Mixed Finite Element Methods
10.07.2017	Zihan Liu	Local Projection Stabilization
24.07.2017

Report

• The report should be submitted in electronical form preferrably using Latex.
• It should serve as a summary of your presentation containing between 5 and 10 pages. In particular, make sure to write in the way you would write this yourself and don't copy & paste from the reference.
• Don't forget to include citations to results you are using and don't prove.
• Submission via e-mail until August 16th.

Literature

• Grossmann, Roos, Stynes: Numerical Treatment of partial Differential Equations, Springer, 2007.
• Quarteroni, Valli: Numerical approximation of partial differential equations. Springer, 2008.
• Johnson: Numerical solution of partial differential equations by the finite element method. Dover, 2009.
• Brezzi, Fortin: Mixed and Hybrid Finite Element Methods, Springer 1991