97-44
Evolution Galerkin Methods for Hyperbolic Systems in Two Space Dimensions
by Luk\xe1cov\xe1-Medvidov\xe1, M. (Brünn); Morton, K.W.; Warnecke, G.
Preprint series: 97-44, Preprints
- MSC:
- 35L05 Wave equation
- 65M06 Finite difference methods
- 35L45 Initial value problems for hyperbolic systems of first-order PDE
- 35L65 Conservation laws
- 65M25 Method of characteristics
- 65M15 Error bounds
Abstract: The subject of the paper is the analysis of three new evolution Galerkin schemes for the system of hyperbolic equations, and particularly for the wave equation system. 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 transported along the characteristic cone and then projected onto a finite element space. A numerical comparison of the new methods with already existing methods based on the use of the bicharacteristics as well as the commonly used finite volume methods is given. We show the stability properties of the schemes and derive error estimates.
Keywords: genuinely multidimensional schemes, hyperbolic systems, wave equation, Euler equations, evolution Galerkin schemes