SUB-OPTIMAL CONVERGENCE OF DISCONTINUOUS GALERKIN METHODS WITH CENTRAL FLUXES FOR LINEAR HYPERBOLIC EQUATIONS WITH EVEN DEGREE POLYNOMIAL APPROXIMATIONS

• 作者: Yong Liu Chi-Wang Shu Mengping Zhang
• 来源期刊: 计算数学（英文版）
• 年，卷（期）: 2021,（4）
• 页码范围: 518-537
• 页数: 20页
• 语种: 英文
• DOI: 10.4208/jcm.2002-m2019-0305

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 L2-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.