After successful completion of the course, students are able to understand the basic analytic and numerical structures of hyperbolic conservation laws. Also, they can give a presentation about this topic and to write a seminar paper.

1. scalar conservation laws 2. linear hyperbolic systems, examples of nonlinear systems 3. shock and rarefaction waves, contact discontinuities 4. numerical methods for linear equations 5. computing discontinuous solutions 6. conservative methods for nonlinear problems 7. Godunov-scheme 8. appropriate Riemann solvers 9. nonlinear stability 10.high resolution methods 11.kinetic schemes for hyperbolic conservation laws 12.boundary conditions

presentation by the participating students (blackboard or beamer),

discussion of the weekly seminar by the whole "class",

write-up of a seminar paper

good oral presentation, written seminar report, regular participation

* lecture notes of C. Schmeiser * Randall J. LeVeque: Numerical Methods for Conservation Laws, Birkhäuser, 1990 * R.J. Leveque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002

numerical analysis, differential equations. Particularly suited for students in the 5th semester - as a parallel course to "partial differential equations"