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Hyperbolic systems, entropy a the method of finite volumes. (English) Zbl 1046.35073

After a brief introduction to the problems of existence and uniqueness of weak solutions for hyperbolic systems the author explains how the method of finite elements can be used for numerical solution. This method seems more natural in the cases when discontinuities in solutions can be expected. Another important property of this method is its ability to add to the scheme so called numerical viscosity by means of upwinding which eventually influences the ability of the scheme to find among all possible solutions just the physical, entropical ones, which are of the main interest.

MSC:

35L65 Hyperbolic conservation laws
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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