Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for even degree polynomial approximations
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In this paper, we theoretically and numerically verify that the discontinuous Galerkin (DG) methods with central fluxes on non-uniform meshes have sub-optimal convergence properties when measured in the L^2-norm for even degree polynomial approximations. On uniform meshes, the optimal error estimates are provided for arbitrary number of cells in one and multi-dimensions, improving previous results. The theoretical findings are found to be sharp and consistent with numerical results.
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