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nonconforming finite element Method for Gradient flow Equations in Robin Conditions

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Journal of Mathematics and System Science 2014年第5期4卷 315-326页

作者： Changhui Yao Shaorong Li School of Mathematics and Statistics Zhengzhou University Zhengzhou City P.R. China Foundation Department Shangqiu Vocational College Shangqiu 476000 China

In this paper, Crouzeix-Raveart type nonconforming rectangular element is applied to the Mumford-Shah functional for image segmentation subjected to Robin boundary conditions. Meanwhile, by using the special orthogonality of this element＇s basic functions, the convergence analysis for L2-norm and broken H1-norm with semi-implicit scheme is presented. And the error order is improved to the optimal, too.

关键词： Image segmentation nonconforming finite element Robbin boundary conditions error estimate.

HIGHLY nonconforming finite element APPROXIMATIONS FOR A FOURTH ORDER VARIATIONAL INEQUALITY WITH CURVATURE OBSTACLE

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Journal of Systems Science & Complexity 2005年第1期18卷 136-142页

作者： SHIDongyang CHENShaochun IchiroHagiwara DepartmentofMathematics ZhengzhouUniversityZhengzhou450052China TokyoInstituteofTechnology 2-12-1OhokayamaMegroTokyo152-8552Japan

The purpose of this paper is to obtain the optimal error estimates of O(h) for the highly nonconforming elements to a fourth order variational inequality with curvature obstacle in a convex domain with simply supported boundary by using the novel function splitting method and the orthogonal properties of the nonconforming finite element ***'s element approximation is our special case.

关键词： variational inequality curvature obstacle nonconforming finite element optimal error estimation

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ON THE ANISOTROPIC ACCURACY ANALYSIS OF ACMES nonconforming finite element

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Journal of Computational Mathematics 2005年第6期23卷 635-646页

作者： Dong-yang Shi Shi-peng Mao Shao-chun Chen Department of Mathematics Zhengzhou University Zhengzhou 450052 China

The main aim of this paper is to study the superconvergence accuracy analysis of the famous ACM＇s nonconforming finite element for biharmonic equation under anisotropic meshes. By using some novel approaches and techniques, the optimal anisotropic interpolation error and consistency error estimates are obtained. The global error is of order O（h^2）. Lastly, some numerical tests are presented to verify the theoretical analysis.

关键词： Superconvergence nonconforming finite element Anisotroplc interpolation error Consistency error

AN IMPROVED AXISYMMETRIC WILSON nonconforming finite element METHOD FOR STRESS ANALYSIS

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2000年第3期 47-53页

作者：张武 DESAI C.S. YONG Y.K.

The Wilson and Taylor elements Q6 and QM6, the representative nonconforming finite element method(FEM), have been successfully developed and implemented in the finite element code SAP for improved displacement and stress analysis. This paper formulates an improved convergent nonconforming axisymmetric element AQM6 over the corresponding axisymmetric Q6 and QM6 elements. The proposed modified nonconforming axisymmetric element AQM6 satisfies the engineering patch test condition for convergence, and also meets the condition for suppression of spurious shear stress by using a special remedying procedure. The numerical test results are in agreement with the element performance.

关键词： nonconforming finite element axisymmetric Wilson element patch test condition convergence spurious shear stress

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Z1期 299-314页

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

An anisotropic nonconforming finite element method is presented for a class of nonlinearSobolev *** optimal error estimates and supercloseness are obtained for bothsemi-discrete and fully-discrete approximate schemes,which are the same as the traditionalfinite element *** addition,the global superconvergence is derived through thepostprocessing *** experiments are included to illustrate the feasibilityof the proposed method.

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

A nonconforming ANISOTROPIC finite element APPROXIMATION WITH MOVING GRIDS FOR STOKES PROBLEM

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Journal of Computational Mathematics 2006年第5期24卷 561-578页

作者： Dong-yang Shi Yi-ran Zhang Department of Mathematics Zhengzhou University Zhengzhou 450052 China School of Mathematical Science Peking University Beijing 100871 China

This paper is devoted to the five parameters nonconforming finite element schemes with moving grids for velocity-pressure mixed formulations of the nonstationary Stokes problem in 2-D. We show that this element has anisotropic behavior and derive anisotropic error estimations in some certain norms of the velocity and the pressure based on some novel techniques. Especially through careful analysis we get an interesting result on consistency error estimation, which has never been seen for mixed finite element methods in the previously literatures.

关键词： Stokes problem nonconforming finite element Anisotropy Moving grids Error estimate.

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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A nonconforming Rectangular finite element Analysis for the Stokes Problem

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Chinese Quarterly Journal of Mathematics 2009年第4期24卷 621-627页

作者： XIAO Liu-chao CHEN Shao-chun College of Science Henan University of Technology Zhengzhou 450001 China Department of Mathematics Zhengzhou University Zhengzhou 450001 China

A nonconforming rectangular finite element is presented, which satisfies the discrete B-B condition for the Stokes problem. And the element has two order convergence rate for the velocity and pressure.

关键词： Stokes problem nonconforming finite element B-B condition

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A COUPLED METHOD COMBINING CROUZEIX-RAVIART nonconforming AND NODE CONFORMING finite element SPACES FOR BOIT CONSOLIDATION MODEL

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Journal of Computational Mathematics 2024年第4期42卷 911-931页

作者： Yuping Zeng Mingchao Cai Liuqiang Zhong School of Mathematics Jiaying UniversityMeizhou 514015China Department of Mathematics Morgan State University1700 E Cold Spring LnBaltimoreMD 21251USA School of Mathematical Science South China Normal UniversityGuangzhou 520631China

A mixed finite element method is presented for the Biot consolidation problem in *** precisely,the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements,while the fuid pressure is approximated by using the node conforming finite *** well-posedness of the fully discrete scheme is established,and a corresponding priori error estimate with optimal order in the energy norm is also *** experiments are provided to validate the theoretical results.

关键词： Poroelasticity nonconforming finite element Inf-sup condition A priori error estimate