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Numerical Methods for Hyperbolic Equations (Sommersemester 2019)

Master Mathematics, Technical Mathematics, Economical Mathematics

We present basic theory for equations in conservation form and the fundamental principle to derive numerical methods. As an application we focus on compressible flow equations and Maxwell equations.

Requirements: Numerical Methods for Differential Equations.

Exercises and helpful course materials can be found here: ILIAS

Introductionary course

There will be a short course in 'Basics in Finite Elements' and 'Solving Linear Equations' by Dr. Anzt and me. It is a course in the new KIT-Centre MATHSEE and is designed for engineers. This course will replace the dates in the first week and is recommended as an introduction.

Basics in Discretisations of PDEs. Dates: Wed/Thu 24./25.4.2019, 14:00-17:15.

Vorlesung: Montag 11:30-13:00 SR 3.61 Beginn: 29.4.2019, Ende: 24.7.2019
Dienstag 11:30-13:00 (14-tägig) SR 3.61
Übung: Dienstag 11:30-13:00 (14-tägig) SR 3.61 Beginn: 8.5.2019, Ende: 24.7.2019
Dozent, Übungsleiter Prof. Dr. Willy Dörfler
Sprechstunde: Montags, 14:15-15:15 Uhr oder nach Vereinbarung.
Zimmer 3.013 Kollegiengebäude Mathematik (20.30)
Email: willy.doerfler at kit.edu
Übungsleiterin M.Sc. Mariia Sukhova
Sprechstunde: nach Vereinbarung
Zimmer 3.010 Kollegiengebäude Mathematik (20.30)
Email: mariia.sukhova@kit.edu


Derivation of equations in conservation form. Shocks, Rarefaction waves, weak solutions. Aspects of existence and regularity theory. Discretization of conservation laws with Finite Volume and Discontinuous Galerkin Methods Applications.


Examination: Oral examination.

6 LP


  • J. S. Hesthaven: Numerical Methods for Conservation Laws
  • J. S. Hesthaven, T. Warburton: Nodal discontinuous Galerkin methods
  • D. Kröner: Numerical Schemes for Conservation Laws
  • R. Leveque: Numerical Methods for Conservation Laws