Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system

The subject of the paper is the derivation and analysis of third order nite volume evolution Galerkin schemes for the two-dimensional wave equation system. To achieve this the rst order approximate evolution operator is considered. A recovery stage is carried out at each level to generate a piecewise polynomial approximation ~ U n = RhU n 2 S h from the piecewise constantU 2 S h , to feed into the calculation of the uxes. We estimate the truncation error and give numerical examples to demonstrate the higher order behaviour of the scheme for smooth solutions.