Fourier Type Error Analysis of the Direct Discontinuous Galerkin Method and Its Variations for Diffusion Equations

被引：0
作者：
Mengping Zhang
Jue Yan
机构：
[1] University of Science and Technology of China,Department of Mathematics
[2] Iowa State University,Department of Mathematics
来源：
Journal of Scientific Computing | 2012年 / 52卷
关键词：
Discontinuous Galerkin method; Diffusion equation; Stability; Consistency; Convergence; Supraconvergence;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we present Fourier type error analysis on the recent four discontinuous Galerkin methods for diffusion equations, namely the direct discontinuous Galerkin (DDG) method (Liu and Yan in SIAM J. Numer. Anal. 47(1):475–698, 2009); the DDG method with interface corrections (Liu and Yan in Commun. Comput. Phys. 8(3):541–564, 2010); and the DDG method with symmetric structure (Vidden and Yan in SIAM J. Numer. Anal., 2011); and a DG method with nonsymmetric structure (Yan, A discontinuous Galerkin method for nonlinear diffusion problems with nonsymmetric structure, 2011). The Fourier type L2 error analysis demonstrates the optimal convergence of the four DG methods with suitable numerical fluxes. The theoretical predicted errors agree well with the numerical results.
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页码：638 / 655
页数：17
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