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 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 Ũ n = R h U n ∈ from the piecewise constant U n ∈ , 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.