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

**Series:** 1997-44, Preprints

- MSC:
- 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

**Abstract:**

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.

**Keywords:**

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