Sub-Optimal Convergence of Discontinuous Galerkin Methods with Central Fluxes for Linear Hyperbolic Equations with Even Degree Polynomial Approximations
Year: 2021
Author: Yong Liu, Chi-Wang Shu, Mengping Zhang
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 4 : pp. 518–537
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2002-m2019-0305
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 4 : pp. 518–537
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Discontinuous Galerkin method Central flux Sub-optimal convergence rates.