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nonconforming finite element APPROXIMATIONS TO THE UNILATERAL PROBLEM

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Journal of Computational Mathematics 1999年第1期17卷 15-24页

作者： Lie-heng Wang(State Key Laboratory of Scientific and Engeneering Computing, ICMSEC,Chinese Academy of Sciences, Beijing 100080, China) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京

The nonconforming finite element (two Crouzeix-Raviart linear elements and Wilson element) approximations to the unilateral problem are considered. The error bounds for these elements are obtained in the appropriate a... 详细信息

关键词： unilateral problem nonconforming finite element

nonconforming finite element methods on quadrilateral meshes

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Science China Mathematics 2013年第12期56卷 2599-2614页

作者： HU Jun ZHANG ShangYou LMAM and School of Mathematical Sciences Peking University Department of Mathematical Sciences University of DelawareNewark DE 19716 USA

It is well known that it is comparatively difficult to design nonconforming finite elements on quadri- lateral meshes by using Gauss-Legendre points on each edge of triangulations. One reason lies in that these de- grees of freedom associated with these Gauss-Legendre points are not all linearly independent for usual expected polynomial spaces, which explains why only several lower order nonconforming quadrilateral finite elements can be found in literature. The present paper proposes two families of nonconforming finite elements of any odd order and one family of nonconforming finite elements of any even order on quadrilateral meshes. Degrees of freedom are given for these elements, which are proved to be well-defined for their corresponding shape function spaces in a unifying way. These elements generalize three lower order nonconforming finite elements on quadri- laterals to any order. In addition, these nonconforming finite element spaces are shown to be full spaces which is somehow not discussed for nonconforming finite elements in literature before.

关键词： nonconforming finite element rectangle

AN ANISOTROPIC nonconforming finite element SCHEME WITH MOVING GRIDS FOR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

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Journal of Systems Science & Complexity 2011年第5期24卷 1020-1032页

作者： Dongyang SHI Lin WANG Department of Mathematics Zhengzhou University Zhengzhou 450052 China Department of Basic Henan Mechanical and Electrical Engineering College Xinxiang 453002 China

A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature.

关键词： Anisotropic meshes error estimates moving grids nonconforming finite element parabolicintegro-differential equations

AN ANISOTROPIC nonconforming finite element WITH SOME SUPERCONVERGENCE RESULTS

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Journal of Computational Mathematics 2005年第3期23卷 261-274页

作者： Dong-yangShi Shi-pengMao Shao-chunChen DepartmentofMathematics ZhengzhouUniversityZhenzhou450052China

The main aim of this paper is to study the error estimates of a nonconforming finite element with some superconvergence results under anisotropic meshes. The anisotropic interpolation error and consistency error estimates are obtained by using some novel approaches and techniques, respectively. Furthermore, the superclose and a superconvergence estimate on the central points of elements are also obtained without the regularity assumption and quasi-uniform assumption requirement on the meshes. Finally, a numerical test is carried out, which coincides with our theoretical analysis.

关键词： Anisotropic meshes nonconforming finite element Interpolation error and consistency error estimates Superclose Superconvergence

AN ANISOTROPIC nonconforming finite element METHOD FOR APPROXIMATING A CLASS OF NONLINEAR SOBOLEV EQUATIONS

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Journal of Computational Mathematics 2009年第2期27卷 299-314页

作者： Dongyang Shi Haihong Wang Yuepeng Du Department of Mathematics Zhengzhou University Zhengzhou 450052 China Department of Computer Nanyang Institute of Technology Nanyang 473004 China

An anisotropic nonconforming finite element method is presented for a class of nonlinear Sobolev equations. The optimal error estimates and supercloseness are obtained for both semi-discrete and fully-discrete approximate schemes, which are the same as the traditional finite element methods. In addition, the global superconvergence is derived through the postprocessing technique. Numerical experiments are included to illustrate the feasibility of the proposed method.

关键词： Nonlinear Sobolev equations Anisotropic nonconforming finite element Supercloseness Global superconvergence.

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

Quadratic nonconforming finite element method for 3D Stokes equations on cuboid meshes

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Applied Mathematics(A Journal of Chinese Universities) 2016年第1期31卷 21-36页

作者： ZHOU Xin-chen MENG Zhao-liang WANG Xiao-shan LUO Zhong-xuan School of Mathematical Sciences Dalian University of TechnologyDalian 116024China School of Software Dalian University of TechnologyDalian 116024China

In this paper, the quadratic nonconforming brick element （MSLK element） intro- duced in [10] is used for the 3D Stokes equations. The instability for the mixed element pair MSLK-P1 is analyzed, where the vector-valued MSLK element approximates the velocity and the piecewise P1 element approximates the pressure. As a cure, we adopt the piecewise P1 macroelement to discretize the pressure instead of the standard piecewise P1 element on cuboid meshes. This new pair is stable and the optimal error estimate is achieved. Numerical examples verify our theoretical analysis.

关键词： Stokes equations nonconforming finite element macroelement stability.

EQ_1^(rot) nonconforming finite element approximation to Signorini problem

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Science China Mathematics 2013年第6期56卷 1301-1311页

作者： SHI DongYang XU Chao Department of Mathematics Zhengzhou University Department of Mathematics and Physics Luoyang Institute of Science and Technology

Abstract In this paper, we apply EQ1^rot nonconforming finite element to approximate Signorini problem. If 5 the exact solution u EQ1^rot, the error estimate of order O（h） about the broken energy norm is obtained for quadrilateral meshes satisfying regularity assumption and bi-section condition. Furthermore, the superconver- gence results of order EQ1^rot are derived for rectangular meshes. Numerical results are presented to confirm the considered theory.

关键词： Signorini problem nonconforming finite element superconvergence error estimate

A new a priori error estimate of nonconforming finite element methods

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Science China Mathematics 2014年第5期57卷 887-902页

作者： HU Jun MA Rui1 SHI ZhongCi LMAM and School of Mathematical Sciences Peking University LSEC ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

This paper is devoted to a new error analysis of nonconforming finite element *** with the classic error analysis in literature,only weak continuity,the F-E-M-Test for nonconforming finite element spaces,and basic Hm regularity for exact solutions of 2m-th order elliptic problems under consideration are *** analysis is motivated by ideas from a posteriori error estimates and projection average *** main ingredient is a novel decomposition for some key average terms on(n.1)-dimensional faces by introducing a piecewise constant projection,which defines the generalization to more general nonconforming finite elements of the results in *** analysis and results herein are conjectured to apply for all nonconforming finite elements in literature.

关键词： nonconforming finite element consistency error error estimate