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MATHEMATICAL ANALYSIS FOR QUADRILATERAL ROTATED Q_1 ELEMENT Ⅱ: POINCARE INEQUALITY AND TRACE INEQUALITY

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Journal of Computational Mathematics 2003年第3期21卷 277-286页

作者： Ping-bing Ming zhong-ci shi Institute of Computational Mathematics Chinese Academy of Sciences Beijing 100080 China

This is the second part of the paper for the mathematical study of nonconforming rotated Q1 element (NRQ1 hereafter) on arbitrary quadrilateral meshes. Some Poincare Inequalities are proved without assuming the quasi-... 详细信息

关键词： Quadrilateral rotated Q1 element Poincare inequality Trace inequality.

P1-NONCONFORMING QUADRILATERAL FINITE VOLUME ELEMENT METHOD AND ITS CASCADIC MULTIGRID ALGORITHM FOR ELLIPTIC PROBLEMS

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Journal of Computational Mathematics 2006年第1期24卷 59-80页

作者： Hong-ying Man zhong-ci shi LSEC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of Mathematics Beijing institute of Technology Beijing 100081 China

In this paper, we discuss the finite volume element method of P1-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition. An optimal cascadic multigrid algorithm is proposed to solve the non-symmetric large-scale system resulting from such discretization. Numerical experiments are reported to support our theoretical results.

关键词： finite volume element method cascadic multigrid Elliptic problems

A NOTE ON THE QUADRILATERAL MESH CONDITION RDP(N,ψ)

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Journal of Computational Mathematics 2007年第1期25卷 27-30页

作者： Dongyang shi zhong-ci shi Jingzhu Wu Department of Mathematics Zhengzhou University Zhengzhou 450052 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

The main aim of this paper is to show that the quadrilateral mesh condition RDP（N, ψ） is only sufficient but not necessary for the optimal order error estimate of the Q isoparametric element in the Hi norm.

关键词： Isoparametric finite element Optimal order error estimate Quadrilateral meshcondition.

EXPLIciT ERROR ESTIMATES FOR MIXED AND NONCONFORMING FINITE ELEMENTS

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Journal of Computational Mathematics 2009年第4期27卷 425-440页

作者： shipeng Mao zhong-ci shi LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be ex- tended to the nonconforming P1 scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods.

关键词： Mixed finite element Nonconforming finite element Explicit error estimate,Maximal angle condition.

Optimal L_∞ Estimates for Galerkin Methods for Nonlinear Singular Two-point Boundary Value Problems

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Acta Mathematicae Applicatae Sinica 2015年第3期31卷 719-728页

作者： Xu ZHANG zhong-ci shi Nanjing University of Aeronautics and Astronautics LSEC ICMSEC Academy of Mathematics and Systems Science CAS

In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining full superconvergence uniformly at all nodal points, we introduce local mesh refinements. Then we extend these results to a class of nonlinear problems. Finally, we present some numerical results which confirm our theoretical conclusions.

关键词： singular two-point boundary value problems symmetric Galerkin method maximum norm error estimate superconvergence local mesh refinement

Hexahedral constraint-free finite element method on meshes with hanging nodes

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Science China Mathematics 2019年第12期62卷 2591-2616页

作者： Xuying Zhao zhong-ci shi LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingNCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

Nonconforming grids with hanging nodes are frequently used in adaptive finite element comput at *** all earlier works on such methods,proper cons train ts should be enforced on degrees of freedom on edges/faces with hanging nodes to keep continuity,which yield numerical computations much *** 2014,Zhao et al.(2014)presented quadrilateral constraint-free finite element methods on quadrilateral grids with hanging *** paper further develops a hexahedral constraint-free finite element method on hexahedral grids with hanging nodes,which is of greater challenge than the two-dimensional ***-based a posteriori error reliability and efficiency are also established in this paper.

关键词： adaptive finite element a posteriori error estimate hexahedral nonconforming element hangingnode

THE BEST L2 NORM ERROR ESTIMATE OF LOWER ORDER FINITE ELEMENT METHODS FOR THE FOURTH ORDER PROBLEM

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Journal of Computational Mathematics 2012年第5期30卷 449-460页

作者： Jun Hu zhong-ci shi LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871China LSEC ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In the paper, we analyze the L2 norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L2 norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the finite element solution. The result holds for most of the popular lower order finite element methods in the literature including： the Powell-Sabin C1 -P2 macro element, the nonconforming Morley element, the C1 -Q2 macro element, the nonconforming rectangle Morley element, and the nonconforming incomplete biquadratic element. In addition, the result actually applies to the nonconforming Adini element, the nonconforming Fraeijs de Veubeke elements, and the nonconforming Wang- Xu element and the Wang-shi-Xu element provided that the saturation condition holds for them. This result solves one long standing problem in the literature： can the L2 norm error estimate of lower order finite element methods of the fourth order problem be two order higher than the error estimate in the energy norm？

关键词： L2 norm error estimate Energy norm error estimate Conforming Noncon-forming The Kirchhoff plate.

SOME n-RECTANGLE NONCONFORMING ELEMENTS FOR FOURTH ORDER ELLIPTIC EQUATIONS

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Journal of Computational Mathematics 2007年第4期25卷 408-420页

作者： Ming Wang zhong-ci shi Jinchao Xu LMAM School of Mathematical Sciences Peking University Beijing 100080 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China School of Mathematical Sciences Peking University Beijing 100080 China and Department of Mathematics Pennsylvania State University USA

In this paper, three n-rectangle nonconforming elements are proposed with n ≥ 3. They are the extensions of well-known Morley element, Adini element and Bogner-Fox-Schmit element in two spatial dimensions to any higher dimensions respectively. These elements are all proved to be convergent for a model biharmonic equation in n dimensions.

关键词： Nonconforming finite element Forth order elliptic equation Biharmonic.

THE GENERALIZED MAXIMUM ANGLE CONDITION FOR THE Q1 ISOPARAMETRIC ELEMENT

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Journal of Computational Mathematics 2006年第1期24卷 1-8页

作者： Jun Hu zhong-ci shi LSEC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Graduate School of the Chinese Academy of Sciences Beijing 100080 China

We consider the quadrilateral Q1 isoparametric element and establish an optimal error estimate in H^1 norm for the interpolation operator under a weaker mesh condition which admits anisotropic quadrilaterals and allow... 详细信息

关键词： Quadrilateral mesh Q1 isoparametric element Generalized maximum angle condition