Finite Element methods for hyperbolic systems (Advanced Finite Element Methods MA4303)

The lecture will be devoted to the numerical approximation of hyperbolic conservation laws using finite difference, finite elements and discontinuous Galerkin discretization in space. Explicit and implicit time discretisation will be considered. Iterative methods for the non linear system resulting from implicit time discretisation will also be introduced. After introducing the methods in the scalar case, they will be applied to systems with increasing difficulties (Maxwell, Euler, MHD). An exercise class is associated to the lecture where as well analytical exercises as coding exercises in Python will be proposed.

Literature

• A. Ern and J.-L. Guermond: Theory and Practice of Finite Elements, Springer 2004.
• J. S. Hesthaven and T. Warburton: Nodal Discontinuous Galerkin methods, Springer, 2008.
• E. Godlewski and P.A. Raviart: Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer, 1996.
• R. J. Leveque: Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, 2002.

Lecturers

• Lectures: Prof. Dr. Eric Sonnendrücker. Monday 8:30-10:00 MI 03.06.011
• Exercises: Dr. Ahmed Ratnani. Wednesday 10:15-11:45 MI 03.10.011

Lecture Notes

• Lecture Notes

Exercises

• Exercise sheet 1
• Exercise sheet 2
• Exercise sheet 3
• Exercise sheet 4

• Python tutorial and exercises

-- EricSonnendruecker - 23 Sep 2014