Fourier Type Error Analysis of the Direct Discontinuous Galerkin Method and Its Variations for Diffusion Equations
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- 作者：Mengping Zhang (1) mpzhang@ustc.edu.cn
Jue Yan (2) jyan@iastate.edu - 关键词：Discontinuous Galerkin method – ; Diffusion equation – ; Stability – ; Consistency – ; Convergence – ; Supraconvergence
- 刊名：Journal of Scientific Computing
- 出版年：2012
- 出版时间：September 2012
- 年：2012
- 卷：52
- 期：3
- 页码：638-655
- 全文大小：588.4 KB
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- ISSN：1573-7691
文摘
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 L 2 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.