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Evolution Galerkin methods for multidimensional hyperbolic systems. (English) Zbl 0968.65070

Bock, Hans Georg (ed.) et al., ENUMATH 97. Proceedings of the 2nd European conference on numerical mathematics and advanced applications held in Heidelberg, Germany, September 28-October 3, 1997. Including a selection of papers from the 1st conference (ENUMATH 95) held in Paris, France, September 1995. Singapore: World Scientific. 445-452 (1998).
Summary: This contribution deals with the genuinely multidimensional numerical schemes for solving systems of hyperbolic equations. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The main idea of the evolution Galerkin methods is the following. The initial function is evolved using the characteristic cone and then projected onto a finite element space. A numerical comparison of the new evolution Galerkin methods with the commonly used finite volume methods is given. Some well-known test problems for the wave equation system and for the Euler equations are presented.
For the entire collection see [Zbl 0949.00502].

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
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