by Lukacova-Medvidova, M., Warnecke, G., Zahaykah, Y..

**Series:** 2004-27, 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

**Abstract:**

The subject of the paper is the derivation of finite volume evolution Galerkin schemes for three-dimensional wave equation system. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The idea is to evolve the initial function using the characteristic cone and then to project onto a finite element space. Numerical experiments are presented to demonstrate the accuracy and the multidimensional behaviour of the solutions. Moreover, we construct further new EG schemes by neglecting the so-called source term, i.e. we mimic Kirchhoff's formula. The numerical test shows that such schemes are more accurate and some of them are of second order.

**Keywords:**

hyperbolic systems, wave equation, evolution Galerkin schemes, recovery stage, finite volume