(Created 2010-07-25.)

FINITE VOLUME METHODS | FMN091 |

**Aim**

The aim of the course is to provide a deeper understanding of the construction and application of modern schemes for conservation laws. The focus is on the interaction between mathematical properties of the model and choice of discrete approximation.

*Knowledge and understanding*

For a passing grade the student must

*Skills and abilities*

For a passing grade the student must

- be able to adapt the methods to varying applications, e.g., shallow water waves, gas dynamics, electromagnetism, ultra sound, etc.

- be able to judge the relevance and accuracy of numerical results.

- report solutions and numerical simulations in written form.

*Judgement and approach*

For a passing grade the student must

- write an algorithmically well structured report in suitable terminology on the numerical approximation of conservation laws.

**Contents**

Hyperbolic conservation laws and their properties (weak solution, energy estimates, symmetrization and entropy, shock waves, Riemann problem, Kruzkov solution, stability in L_1, ...). Numerical methods and their stability (upwind-, central-, and relaxation methods, TVD methods and limiters, error estimation using Kruzkov theory). Simulation of shallow water waves and gas dynamics using CLAWPACK.

**Literature**

1. Randall LeVeque: Finite Volume Methods foir Hyperbolic Problems (ISBN 0 521 00924 3), Cambridge Univ. Press, 2002.

2. Helge Holden and Nils Henrik Risebro: Front Tracking for Hyperbolic Conservation Laws, Springer, New York, 2002.