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Robust a Posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients on Anisotropic Meshes
Zhao, Jikun1; Chen, Shaochun1; Zhang, Bei1; Mao, Shipeng2,3
2015-08-01
Source PublicationJOURNAL OF SCIENTIFIC COMPUTING
ISSN0885-7474
Volume64Issue:2Pages:368-400
AbstractIn this paper, we study a posteriori estimates for different numerical methods of diffusion problems with discontinuous coefficients on anisotropic meshes, in particular, which can be applied to vertex-centered and cell-centered finite volume, finite difference and piecewise linear finite element methods. Based on the stretching ratios of the mesh elements, we improve a posteriori estimates developed by Vohralik (J Sci Comput 46:397-438, 2011), which are reliable and efficient on isotropic meshes but fail on anisotropic ones (see the numerical results of the paper). Without the assumption that the meshes are shape-regular, the resulting mesh-dependent error estimators are shown to be reliable and efficient with respect to the error measured either as the energy norm of the difference between the exact and approximate solutions, or as a dual norm of the residual, as long as the anisotropic mesh sufficiently reflects the anisotropy of the solution. In other words, they are equivalent to the estimates of Vohralik in the case of isotropic meshes and proved to be robust on anisotropic meshes as well. Based on -conforming, locally conservative flux reconstruction, we suggest two different constructions of the equilibrated flux with the anisotropy of mesh, which is essential to the robustness of our estimates on anisotropic meshes. Numerical experiments in 2D confirm that our estimates are reliable and efficient on anisotropic meshes.
KeywordA posteriori error estimates Anisotropic meshes Finite volume method Finite difference method Finite element method Discontinuous coefficients
DOI10.1007/s10915-014-9937-7
Language英语
Funding ProjectNational Natural Science Foundation of China[11371331] ; National Natural Science Foundation of China[11101414] ; National Natural Science Foundation of China[11471329] ; National Natural Science Foundation of China[91130026]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000357343600004
PublisherSPRINGER/PLENUM PUBLISHERS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20301
Collection计算数学与科学工程计算研究所
Corresponding AuthorZhao, Jikun
Affiliation1.Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
2.Chinese Acad Sci, LSEC, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Inst Computat Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Zhao, Jikun,Chen, Shaochun,Zhang, Bei,et al. Robust a Posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients on Anisotropic Meshes[J]. JOURNAL OF SCIENTIFIC COMPUTING,2015,64(2):368-400.
APA Zhao, Jikun,Chen, Shaochun,Zhang, Bei,&Mao, Shipeng.(2015).Robust a Posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients on Anisotropic Meshes.JOURNAL OF SCIENTIFIC COMPUTING,64(2),368-400.
MLA Zhao, Jikun,et al."Robust a Posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients on Anisotropic Meshes".JOURNAL OF SCIENTIFIC COMPUTING 64.2(2015):368-400.
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