Abstract: 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 $\tilde{\uu{U}}^{n}=R_h\uu{U}^n\in S_h^2$ from the piecewise constant $\uu{U}^{n}\in S_h^0$, 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.
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