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High-Order Methods for Hyperbolic Equations

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High-Order Methods for Hyperbolic Equations

Lecturer: Dr. Florian Schneider
Lecture: Thursday, 13.45h-15:15h in 48-582

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In this lecture we study different numerical approaches to obtain numerical schemes with arbitrarily high consistency order for hyperbolic equations. In particular we will investigate the following methods:

- ADER (arbitrary order using derivative schemes), including WENO (weighted essentially non-oscillatory) reconstruction
- Strong-Stability preserving Runge-Kutta schemes
- Runge-Kutta Discontinuous-Galerkin schemes


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

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