Extra seminar Computational Mathematics - Dr. P. Öffner, J. Gutenberg University Mainz

Title: Numerical Methods for Hyperbolic Conservation Laws and Related Equations

Abstract:

Hyperbolic conservation laws play a fundamental role in modeling various physical and chemical processes including fluid mechanics, electromagnetism, and wave phenomena. Since especially nonlinear hyperbolic conservation laws cannot be solved analytically, numerical methods have to be applied. In order to utilize modern computer power efficiently, high-order schemes are considered nowadays, though these methods often lack desired stability properties. One aspect of my work is to improve existing numerical schemes in terms of stability and to construct new stable methods. Therefore, I start my talk by given a short introduction into the topic of solving hyperbolic conservation laws and explain the issues. Afterwards, I focus on stability of high-order schemes, give an overlook of the current state of the art, and explain how to construct entropy conservative schemes in a general way. Finally, I give a short summary of my other research results and an outlook of my future plans paying special attention to my possible research contributions to the goals of Cognigron.