Finite Element and Volume Methods in SoSe 2026

Prof. Dr. Siegfried Müller
Huqing Yang, M.Sc. ✉

Dates

Contents of the course:

Part I: weak solution, shocks, concept of entropy, conservative schemes, Lax-Wendroff theorem, monotone schemes, TVD schemes, finite volume discretization, approximate Riemann solvers, discrete entropy inequality, convergence, numerical treatment of boundary conditions,

Part II: finite element discontinuous Galerkin schemes, limiter, time discretization, TVD property, convergence in the mean, grid adaptation, multiresolution analysis.

Objectives

Specifically, students gain deeper insight in either the numerical treatment of hyperbolic conservation laws using finite volume methods and finite element discontinuous Galerkin methods. Furthermore, students are able to describe the basic concepts of the convergence analysis.

Exercises

For the exam admission everyone is required to achieve 50% of the possible points in the exercises and present an exercise at least once in class.

All exercise sheets are uploaded to the RWTHmoodle course room.