Discontinuous Galerkin Methods

What it is about

You will obtain an introduction to Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations. In the end you will be able to derive DG formulations for elliptic, parabolic and hyperbolic problems, evaluate their stability and convergence properties, and practically implement DG schemes.

What you will be able to do

• Derive DG formulations for various PDE prototype problems
• Assess stability and convergence properties of DG schemes
• Understand a priori error estimates
• Apply DG methods for hyperbolic conservation laws
• Use time integration with strongly stability-preserving Runge–Kutta methods
• Use Riemann solvers and limiters in DG schemes
• Implement simple DG methods in Matlab

What the module consists of

• VorlesungIntroduction to mathematical concepts and numerical methods; parts of the implementation will be discussed
• ÜbungDeepening of the lecture material and practical implementation in small Matlab programs

Teaching method

• VorlesungPresentation of the mathematical concepts and numerical procedures
• Übungen mit ProgrammieraufgabenPractical realization and deepening of the methods in Matlab