## Numerical Methods for Partial Differential Equations

### A. Meister

#### Type of the course

Lecture: 4 hours per week
Exercise: 2 hours per week
Open programming exercise: 4 hours per week

#### Time and place

Lecture:
Monday 9.15-10.45 -- Room 421
Wednesday 9.15-10.45 -- Room 421

Exercise:
Monday 13.15-14.45 -- Room 2420

Open programming exercise:
Friday 9.15-10.45 -- Room 2421
Friday 11.15-12.45 -- Room 2421

#### Begin of the course

Wednesday, April 11th, 9.15 -- Room 421

#### Content

This course will introduce the basic aspects of partial different equations as well as their numerical treatment. Thereby, we will focus on hyperbolic systems of equations which are fundamental with respect to practical applications in fluid mechanics.

#### Required previous knowledge

In order to follow the content of the course it is necessary to have foundamental knowledge of the following preceding courses: Numerical Methods I and II as well as Numerical Methods for Ordinary Differential Equations.

Furthermore, here you find the With load blatt6a3.mat the variables xref, rhoref, vref and pref will be loaded into matlab's workspace.

#### Certification

A certification of a successful participation will be given to each student from abroad who has reached 50% of the maximum number of points within the weekly written exercises. Local bachelor as well as master students have to pass additionally an oral examination.

Exercise 1 (pdf)
Exercise 2 (pdf)
Exercise 3 (pdf)
Exercise 4 (pdf)
Exercise 5 (pdf)
Exercise 6 (pdf)
Exercise 7 (pdf)

#### Literature

• K. Burg, H. Haf, F. Wille, A. Meister: Partielle Differentialgleichungen und funktionalanalytische Grundlagen, Vieweg+Teubner.
• A. Meister, J. Struckmeier: Hyperbolic Partial Differential Equations, Vieweg.
• C. Hirsch: Numerical Computation of Internal and External Flows, Part 1 and 2, Wiley.
• H. Kuhlmann: Strömungsmechanik, Pearson Studium.
• E. F. Toro: Riemann Solvers and Numerical Methods for Fluid Dynamics , Springer.
• R. J. LeVeque: Finite Volume methods for Hyperbolic Problems , Cambridge University Press.
• D. Kröner: Numerical Schemes for Conservation Laws , Teubner.
• A. J. Chorin, J. E. Marsden: A Mathematical Introduction to Fluid Mechanics , Springer.