Dispersion and Dissipation Errors of Two Fully Discrete Discontinuous Galerkin Methods

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	Dispersion and Dissipation Errors of Two Fully Discrete Discontinuous Galerkin Methods
	Yang, He ; Li, Fengyan ; Qiu, Jianxian ; Qiu JX(邱建贤)
刊名	http://dx.doi.org/10.1007/s10915-012-9647-y
	2013
关键词	FINITE-ELEMENT METHODS SCALAR HYPERBOLIC EQUATION CONSERVATION-LAWS WAVE-EQUATION BEHAVIOR GRIDS
英文摘要	NSF CAREER [DMS-0847241]; Alfred P. Sloan Research Fellowship; National Science Foundation of China [10931004]; ISTCP of China [2010DFR00700]; The dispersion and dissipation properties of numerical methods are very important in wave simulations. In this paper, such properties are analyzed for Runge-Kutta discontinuous Galerkin methods and Lax-Wendroff discontinuous Galerkin methods when solving the linear advection equation. With the standard analysis, the asymptotic formulations are derived analytically for the discrete dispersion relation in the limit of K=kh -> 0 (k is the wavenumber and h is the meshsize) as a function of the CFL number, and the results are compared quantitatively between these two fully discrete numerical methods. For Lax-Wendroff discontinuous Galerkin methods, we further introduce an alternative approach which is advantageous in dispersion analysis when the methods are of arbitrary order of accuracy. Based on the analytical formulations of the dispersion and dissipation errors, we also investigate the role of the spatial and temporal discretizations in the dispersion analysis. Numerical experiments are presented to validate some of the theoretical findings. This work provides the first analysis for Lax-Wendroff discontinuous Galerkin methods.
语种	英语
出版者	SPRINGER/PLENUM PUBLISHERS
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91281]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Yang, He,Li, Fengyan,Qiu, Jianxian,et al. Dispersion and Dissipation Errors of Two Fully Discrete Discontinuous Galerkin Methods[J]. http://dx.doi.org/10.1007/s10915-012-9647-y,2013.
APA	Yang, He,Li, Fengyan,Qiu, Jianxian,&邱建贤.(2013).Dispersion and Dissipation Errors of Two Fully Discrete Discontinuous Galerkin Methods.http://dx.doi.org/10.1007/s10915-012-9647-y.
MLA	Yang, He,et al."Dispersion and Dissipation Errors of Two Fully Discrete Discontinuous Galerkin Methods".http://dx.doi.org/10.1007/s10915-012-9647-y (2013).