摘要
In this paper,we theoretically and numerically verify that the discontinuous Galerkin(DG)methods with central fluxes for linear hyperbolic equations 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.
基金
esearch of the first author supported by the China Scholarship Council
Research of the second author supported by NSF grant DMS-1719410
Research of the third author supported by NSFC grant 11871448.