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Mathematical Principles of anisotropic mesh Adaptation

Communications in Computational Physics 2006年第2期1卷 276-310页

作者： Weizhang Huang Department of Mathematics University of KansasLawrenceKS 66045U.S.A

mesh adaptation is studied from the mesh control point of *** principles,equidistribution and alignment,are obtained and found to be necessary and sufficient for a complete control of the size,shape,and orientation of mesh elements.A key component in these principles is the monitor function,a symmetric and positive definite matrix used for specifying the mesh information.A monitor function is defined based on interpolation error in a way with which an error bound is minimized on a mesh satisfying the equidistribution and alignment *** for generating meshes satisfying the conditions are developed and two-dimensional numerical results are presented.

关键词： mesh adaptation anisotropic mesh equidistribution alignment error analysis finite element

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CONVERGENCE ANALYSIS FOR A NONCONFORMING MEMBRANE ELEMENT ON anisotropic meshES

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Journal of Computational Mathematics 2005年第4期23卷 373-382页

作者： Dong-yang Shi Shao-chun Chen Ichiro Hagiwara Department of Mathematics Zhengzhou University Zhengzhou 450052 China Tokyo Institute of Technology 2-12-1 Ohokayama Megro Tokyo 152-8552 Japan

Regular assumption of finite element meshes is a basic condition of most analysis of finite element approximations both for conventional conforming elements and nonconforming elements. The aim of this paper is to present a novel approach of dealing with the approximation of a four-degree nonconforming finite element for the second order elliptic problems on the anisotropic meshes. The optimal error estimates of energy norm and L^2-norm without the regular assumption or quasi-uniform assumption are obtained based on some new special features of this element discovered herein. Numerical results are given to demonstrate validity of our theoretical analysis.

关键词： anisotropic mesh Nonconforming finite element Optimal estimate

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A lumped mass nonconforming finite element method for nonlinear parabolic integro-differential equations on anisotropic meshes

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Applied Mathematics(A Journal of Chinese Universities) 2009年第1期24卷 97-104页

作者： SHI Dong-yang WANG Hui-min LI Zhi-yan Dept. of Math., Zhengzhou Univ., Zhengzhou 450052, China Dept. of Math. Zhengzhou Univ. Zhengzhou China

A lumped mass approximation scheme of a low order Crouzeix-Raviart type noncon- forming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is d... 详细信息

关键词： nonlinear parabolic integro-differential equation nonconforming finite element anisotropic mesh lumped mass error estimate

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anisotropic nonconforming Crouzeix-Raviart type FEM forsecond-order elliptic problems

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Applied Mathematics and Mechanics(English Edition) 2012年第2期33卷 243-252页

作者：石东洋许超 Department of Mathematics Zhengzhou University Department of Mathematics and Physics Luoyang Institute of Science and Technology

The nonconforming Crouzeix-Raviart type linear triangular finite element approximate to second-order elliptic problems is studied on anisotropic general triangular meshes in 2D satisfying the maximal angle condition and the coordinate system condition. The optimal-order error estimates of the broken energy norm and L2-norm are obtained.

关键词： nonconforming finite element elliptic problem anisotropic mesh

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A locking-free anisotropic nonconforming rectangular finite element approximation for the planar elasticity problem

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Applied Mathematics(A Journal of Chinese Universities) 2008年第1期23卷 9-18页

作者： SHI Dong-yang WANG Cai-xia Dept. of Math. Zhengzhou Univ. Zhengzhou 450052 China. Faculty of Math. and Inform. Sci. North China Univ. of Water Conservancy and Electric PowerZhengzhou 450011 China.

This paper deals with a new nonconforming anisotropic rectangular finite element approximation for the planar elasticity problem with pure displacement boundary condition. By use of the special properties of this element, and by introducing the complementary space and a series of novel techniques, the optimal error estimates of the energy norm and the L^2-norm are obtained. The restrictions of regularity assumption and quasi-uniform assumption or the inverse assumption on the meshes required in the conventional finite element methods analysis are to be got rid of and the applicable scope of the nonconforming finite elements is extended.

关键词： anisotropic mesh locking-free nonconforming finite element optimal error estimate complementary space.

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