Lehrinhalte
Runge-Kutta discontinuous Galerkin and space-time discontinuous Galerkin schemes. Their application to (time dependent) linear and non-linear convection diffusion equations, Euler equations and Navier-Stokes-equations. A-priori and a-posteriori error estimates.
Literatur
[list]
[*]Dolejsi, Feistauer: Discontinuous Galerkin Method, Analysis and Applications to Compressible Flow, Springer 2015.
[*]Hesthaven, Warburton: Nodal Discontinuous Galerkin Methods, Algorithms, Analysis and Applications, Springer 2008.
[*]Di Pietro, Ern: Mathematical Aspects of Discontinuous Galerkin Methods, Springer 2012
[/list]
Voraussetzungen
recommended: Lecture on numerical methods for ordinary or partial differential equations or similar
Official Course Description
The Euler and Navier-Stokes equations are accespted as the mathematical models for compressible flow in a wide range of applications. Discontinuous-Galerkin methods are a prmomising class of high order discretization schemes for these problems. The lecture starts with the derivation of discontinuous Galekrin methods and iunvestigates the capability of the schemes for representing elementary properties of solutions, e.g., boundary layers, schock waves, entropy dissipation. Based on these investigations, we analyse the stability of the schemes, develop the basic a-priori and a-posteriori error analysis, and discuss aspects of an efficient implementation. As part of the exercise classes, the implemetation will be discussed in details for some model problems. For this, knowledge of Matlab, Python, or C/C will be required.
Runge-Kutta discontinuous Galerkin and space-time discontinuous Galerkin schemes. Their application to (time dependent) linear and non-linear convection diffusion equations, Euler equations and Navier-Stokes-equations. A-priori and a-posteriori error estimates.
Literatur
[list]
[*]Dolejsi, Feistauer: Discontinuous Galerkin Method, Analysis and Applications to Compressible Flow, Springer 2015.
[*]Hesthaven, Warburton: Nodal Discontinuous Galerkin Methods, Algorithms, Analysis and Applications, Springer 2008.
[*]Di Pietro, Ern: Mathematical Aspects of Discontinuous Galerkin Methods, Springer 2012
[/list]
Voraussetzungen
recommended: Lecture on numerical methods for ordinary or partial differential equations or similar
Official Course Description
The Euler and Navier-Stokes equations are accespted as the mathematical models for compressible flow in a wide range of applications. Discontinuous-Galerkin methods are a prmomising class of high order discretization schemes for these problems. The lecture starts with the derivation of discontinuous Galekrin methods and iunvestigates the capability of the schemes for representing elementary properties of solutions, e.g., boundary layers, schock waves, entropy dissipation. Based on these investigations, we analyse the stability of the schemes, develop the basic a-priori and a-posteriori error analysis, and discuss aspects of an efficient implementation. As part of the exercise classes, the implemetation will be discussed in details for some model problems. For this, knowledge of Matlab, Python, or C/C will be required.
- Lehrende: Herbert Egger
- Lehrende: Jan Giesselmann
Semester: WT 2018/19