Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for linear hyperbolic equations with even degree polynomial approximations

Yong Liu; Chi-Wang Shu; Mengping Zhang

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arXiv · 2001.03825

Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for linear hyperbolic equations with even degree polynomial approximations

Yong Liu·Chi-Wang Shu·Mengping Zhang

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Abstract

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.

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Yong Liu, Chi-Wang Shu, Mengping Zhang. 2020-01-12. Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for linear hyperbolic equations with even degree polynomial approximations. https://arxiv.org/abs/2001.03825

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