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401-3652-00L 12 Credits
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Numerical solution of hyperbolic partiial differential equations

Numerik der hyperbolischen Differentialgleichungen

Lecturers & Examiners: Prof. Dr. Ralf Hiptmair
VVZ CR n/a

Last Updated: 2026-02-05 15:10:13

Abstract

This course treats numerical methods for hyperbolic intial-boundary value problems in one andseveral space dimensions, ranging from wave equations to the equations of gas dynamics.The principal classes of methods discussed in the course are finite volume methods anddiscontinuous Galerkin methods. Exercises involve implementation of numerical methods inMATLAB

Objective

The goal of this course is familiarity with the fundamental ideas and mathematical consideration underlying modern numerical methods for conservation laws and wave equations.

Content

Main topics to be covered in the course: * Scalar conservation laws in one space dimension * Finite vollume methods for scalar conservation laws in 1D * High resolution finite volume methods * Spectral viscosity methods * Systems of conservation laws in 1D * Finite volume methods for systems in 1D * Methods for linear wave equations * Time domain integral equation methods * Finite volume methods for scalar conservation laws in several space dimensions * Discontinuous Galerkin methods in one and several spatial dimensions * Adaptive methods

Resources

Lecture Notes

Lecture slides wiill be made available to the audience

Literature

R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002 D. Kroener: Numerical schemes for conservation laws, Wiley-Teubner, 1997 B. Cockburn: Discontinuous Galerkin Methods for Convection-Dominated Problems, in High Order Methods for Computational Physics, T.J. Barth and H. Deconinck, eds. Springer 1999 E. Tadmor: Entropy stability theory for difference approximations of nonlinear conservation laws and related time dependent problems, Acta Numerica, 2003 M. Feistauer, J. Felcman and I. Straskraba: Mathematical and Computational Methods for Compressible Flow, Clarendon Press 2003

General Information

Language
English
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Numerik der hyperbolischen Differentialgleichungen
  • Mon 13:15-15:00 (HG D 1.2)
  • Wed 08:15-10:00 (HG G 26.1)
  • 27.04 Date 08:15-10:00 (HG D 1.2)
  • 04.05 Date 08:15-10:00 (HG E 33.3)
  • 11.05 Date 08:15-10:00 (HG E 33.3)
4 h weekly
exercise Numerik der hyperbolischen Differentialgleichungen
  • Mon 15:15-17:00 (HG D 1.1)
  • Mon 16:15-17:00 (HG F 3)
2 h weekly

Offered In