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Evolution Galerkin Methods for Hyperbolic Systems in Two Space Dimensions

by Lukácová-Medvidová, M., Morton, K.W., Warnecke, G..

Series: 1997-44, Preprints

35L05 Wave equation
65M06 Finite difference methods
35L45 Initial value problems for first-order hyperbolic systems
35L65 Conservation laws
65M25 Method of characteristics
65M15 Error bounds

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 sys-
tem. 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.

genuinely multidimensional schemes, hyperbolic systems, wave equation, Euler equations, evolution Galerkin schemes