Syllabus academic year 2008/2009
(Created 2008-07-17.)

Higher education credits: 7,5. Grading scale: TH. Level: A (Second level). Language of instruction: The course will be given in English on demand. Optional for: F4, F4fs, F4tvb, M4, Pi4, Pi4bs. Course coordinator: Achim Schroll,, Numerisk analys. Recommended prerequisits: Basic course in numerical analysis and partial differential equations. The course might be cancelled if the numer of applicants is less than 10. Assessment: Homework reports and possibly an oral examination. Further information: The next course is planed for fall 2008. Home page:

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

Knowledge and understanding
For a passing grade the student must

demonstrate deep knowledge of mathematical and numerical difficulties regarding shock waves. The student will obtain deeper understanding of design and application of modern schemes for nonlinear conservation laws.

Skills and abilities
For a passing grade the student must

- independently be able to select, apply and design advanced numerical methods.

- be able to adapt the methods to varying applications f. ex. Shallow water, gas dynamics, electromagnetism, ultra sound, etc

- be able to judge the accuracy of numerical results

Judgement and approach
For a passing grade the student must

- report solutions and numerical simulations in written form.

- write a logically well structured report in suitable terminology on the construction of modern mathematical models and algorithms.

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

Hyperbolic conservation laws and their properties (weak solution, symmetrizer and entropy, Riemann problem). Numerical methods and thier stability (upwind-, central-, and relaxation methods, TVB methods and limiters, error estimation and Kruzkov theory). Simulation of shallow water waves and gas dynamics using CLAWPACK.

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.