Información del curso

Lehrinhalte
* Was are high accuracy/high order Methods?
   - Discontinuous Galerkin Methods: approximation with Polynomials
   - scalar conservation laws, weak formulation
   - numerical fluxes
   - temporal discretization 
* Systems of equations and higher derivatives
   - Poisson equation 
   - incompressible flows: Stokes and Navier-Stokes
   - compressible Euler equations
* Basics on numerical analysis
   - Consistency, Stability and Convergence
* Simulation of flows

Literatur
* J. S. Hesthaven, T. Warburton: Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications; Springer, 2008.
* D. A. Di Pietro, A. Ern: Mathematical Aspects of Discontinuous Galerkin Methods, Springer, 2011.
* R. Hartmann: Numerical Analysis of Higher Order Discontinuous Galerkin Finite Element Methods; lecture notes, http://ganymed.iwr.uni-heidelberg.de/~hartmann/publications/2008/Har08b.pdf .
* R. Hartmann: Discontinuous Galerkin methods for compressible flows: higher order accuracy, error estimation and adaptivity; lecture notes http://ganymed.iwr.uni-heidelberg.de/~hartmann/publications/2005/Har05b.pdf .
* B. Cockburn, On Discontinuous Galerkin methods for convection-dominated problems; lecture notes, http://www.math.umn.edu/~bcockbur//LectureNotes.html.

Voraussetzungen
Basic knowledge in parial differential equations and numerics.