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Anisotropic Meshes and Stabilization Parameter Design of Linear SUPG Method for 2D Convection-Dominated Convection-Diffusion Equations
Di, Yana1,2; Xie, Hehu1,2; Yin, Xiaobo3
2018-07-01
Source PublicationJOURNAL OF SCIENTIFIC COMPUTING
ISSN0885-7474
Volume76Issue:1Pages:48-68
AbstractWe 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.
KeywordConvection-diffusion equation Stabilization parameter SUPG Anisotropic mesh
DOI10.1007/s10915-017-0610-9
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000434711800003
PublisherSPRINGER/PLENUM PUBLISHERS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30535
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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