Anisotropic Meshes and Stabilization Parameter Design of Linear SUPG Method for 2D Convection-Dominated Convection-Diffusion Equations

doi:10.1007/s10915-017-0610-9

	Anisotropic Meshes and Stabilization Parameter Design of Linear SUPG Method for 2D Convection-Dominated Convection-Diffusion Equations
	Di, Yana1,2 ; Xie, Hehu1,2 ; Yin, Xiaobo 3
	2018-07-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	76 期号:1 页码:48-68
摘要	We propose a numerical strategy to generate a sequence of anisotropic meshes and select appropriate stabilization parameters simultaneously for linear SUPG method solving two dimensional convection-dominated convection-diffusion equations. Since the discretization error in a suitable norm can be bounded by the sum of interpolation error and its variants in different norms, we replace them by some terms which contain the Hessian matrix of the true solution, convective field, and the geometric properties such as directed edges and the area of triangles. Based on this observation, the shape, size and equidistribution requirements are used to derive corresponding metric tensor and stabilization parameters. Numerical results are provided to validate the stability and efficiency of the proposed numerical strategy.
关键词	Convection-diffusion equation Stabilization parameter SUPG Anisotropic mesh
DOI	10.1007/s10915-017-0610-9
语种	英语
资助项目	National Natural Science Foundation of China[91630208] ; National Natural Science Foundation of China[11771437] ; National Natural Science Foundation of China[91730302] ; National Natural Science Foundation of China[11771434] ; National Natural Science Foundation of China[91330202] ; National Natural Science Foundation of China[11371026] ; National Natural Science Foundation of China[11001259] ; National Natural Science Foundation of China[11031006] ; National Natural Science Foundation of China[2011CB309703] ; National Natural Science Foundation of China[11671165] ; National Natural Science Foundation of China[91630201] ; Science Challenge Project[TZ2016002] ; Program for Changjiang Scholars and Innovative Research Team in University[IRT13066] ; self-determined research funds of Central China Normal University[CCNU16A02039]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000434711800003
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30535
专题	计算数学与科学工程计算研究所
通讯作者	Yin, Xiaobo
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China
推荐引用方式 GB/T 7714	Di, Yana,Xie, Hehu,Yin, Xiaobo. Anisotropic Meshes and Stabilization Parameter Design of Linear SUPG Method for 2D Convection-Dominated Convection-Diffusion Equations[J]. JOURNAL OF SCIENTIFIC COMPUTING,2018,76(1):48-68.
APA	Di, Yana,Xie, Hehu,&Yin, Xiaobo.(2018).Anisotropic Meshes and Stabilization Parameter Design of Linear SUPG Method for 2D Convection-Dominated Convection-Diffusion Equations.JOURNAL OF SCIENTIFIC COMPUTING,76(1),48-68.
MLA	Di, Yana,et al."Anisotropic Meshes and Stabilization Parameter Design of Linear SUPG Method for 2D Convection-Dominated Convection-Diffusion Equations".JOURNAL OF SCIENTIFIC COMPUTING 76.1(2018):48-68.