### 2003-21

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

**Series:** 2003-21, Preprints

- MSC:
- 35L05 Wave equation
- 65M06 Finite difference methods

**Abstract:**

The subjekt of the paper is the derivation and analysis of third order finite volume evolution Galerkin schemes for the two-dimensional wave equation system. To achieve this the first order approximate evolution operator is considered. A recovery stage is carried out at each level to generate a piecewise polynomial approximation from the piecewise constant, to feed into the calculation of the fluxes. We estimate the truncation error and give numerical examples to demonstrate the higher order behaviour of the scheme for smooth solutions.

**Keywords:**

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