VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.
Numerical solution of hyperbolic partiial differential equations
Numerik der hyperbolischen Differentialgleichungen
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 |
|
4 h weekly |
| exercise | Numerik der hyperbolischen Differentialgleichungen |
|
2 h weekly |