Robust a Posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients on Anisotropic Meshes

doi:10.1007/s10915-014-9937-7

	Robust a Posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients on Anisotropic Meshes
	Zhao, Jikun 1; Chen, Shaochun 1; Zhang, Bei 1; Mao, Shipeng2,3
	2015-08-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	64 期号:2 页码:368-400
摘要	In 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.
关键词	A posteriori error estimates Anisotropic meshes Finite volume method Finite difference method Finite element method Discontinuous coefficients
DOI	10.1007/s10915-014-9937-7
语种	英语
资助项目	National 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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000357343600004
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/20301
专题	计算数学与科学工程计算研究所
通讯作者	Zhao, Jikun
作者单位	1.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
推荐引用方式 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.