High-Order Methods for Hyperbolic Equations (2V, 4.5 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|2||V||Lecture||4.5 CP||28 h||107 h|
|(2V)||4.5 CP||28 h||107 h|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-TEMA] Industrial Mathematics|
The mathematical concepts for the numerical treatment of systems of hyperbolic conservation equations with high order of approximation in place and time are described and investigated. In particular, the following contents are discussed:
- discontinuous Galerkin method,
- ADER method (incl. WENO reconstruction),
- strong stability preserving (SSP) time stepping.
- J. S. Hesthaven, T. Warburton: Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications,
- B. Cockburn: An Introduction to the Discontinuous Galerkin Method for Convection-Dominated Problems,
- E. Toro: Riemann Solvers and Numerical Methods for Fluid Dynamics,
- S. Gottlieb: On High Order Strong Stability Preserving Runge–Kutta and Multi Step Time Discretizations.
Further literature will be announced in the lecture.
Requirements for attendance (informal)
Knowledge from the module [MAT-81-12-M-7] is desirable.
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-80-11A-M-4] Numerics of ODE (M, 4.5 LP)
- [MAT-80-11B-M-4] Introduction to PDE (M, 4.5 LP)
Requirements for attendance (formal)None
References to Course [MAT-81-37-K-7]
|[MAT-81-37-M-7]||High-Order Methods for Hyperbolic Equations||P: Obligatory||2V, 4.5 LP|