Zurück zu den Preprints des Jahres 2004


2004-27

Finite Volume Evolution Galerkin (FVEG) Methods for Three-Dimensinal Wave Equation System

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