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superconvergence.ANALYSIS OF A NONCONFORMING TRIANGULAR ELEMENT ON ANISOTROPIC MESHES

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Journal of Systems Science & Complexity 2007年第4期20卷 536-544页

作者： Dongyang SHI Hui LIANG Caixia WANG Department of Mathematics Zhengzhou University Zhengzhou 450052 China Department of Mathematics Harbin Institute of Technology Harbin 150001 China

The class of anisotropic meshes we conceived abandons the regular assumption. Some distinct properties of Carey＇s element are used to deal with the superconvergence.for a class of two- dimensional second-order elliptic boundary value problems on anisotropic meshes. The optimal results are obtained and numerical examples are given to confirm our theoretical analysis.

关键词： Anisotropic meshes Carey's element Nonconforming superclose superconvergence.

superconvergence.ANALYSIS OF FINITE ELEMENT METHODS FOR OPTIMAL CONTROL PROBLEMS OF THE STATIONARY B(?)NARD TYPE

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Journal of Computational Mathematics 2008年第5期26卷 660-676页

作者： Yanzhen Chang Danping Yang School of Mathematics and System Science Shandong University Jinan 250100 China Department of Mathematics East China Normal University Shanghai 200062 China

In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Benard type under the pointwise control constraint. The states and the co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and the control is approximated by piecewise constant functions. We give the superconvergence.analysis for the control; it is proved that the approximation has a second-order rate of convergence. We further give the superconvergence.analysis for the states and the co-states. Then we derive error estimates in L^∞-norm and optimal error estimates in L^2-norm.

关键词： Optimal control problem The stationary Benard problem Nonlinear coupled system Finite element approximation superconvergence.

superconvergence.OF A DISCONTINUOUS GALERKIN METHOD FOR FIRST-ORDER LINEAR DELAY DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2011年第5期29卷 574-588页

作者： Dongfang Li Chengjian Zhang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China

This paper deals with the discontinuous Galerkin （DG） methods for delay differential equations. By an orthogonal analysis in each element, the superconvergence.results of the methods are derived at nodal points and eigenpoints. Numerical experiments will be carried our to verify the effectiveness and the theoretical results of the proposed methods.

关键词： Discontinuous Galerkin methods Delay differential equations Orthogonalanalysis superconvergence.

CONVERGENCE AND superconvergence.ANALYSIS OF LAGRANGE RECTANGULAR ELEMENTS WITH ANY ORDER ON ARBITRARY RECTANGULAR MESHES

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Journal of Computational Mathematics 2014年第2期32卷 169-182页

作者： Mingxia Li Xiaofei Guan Shipeng Mao School of Science China University of Geosciences (Beijing) Beijing 100083 China Department of Mathematics Tongji University Shanghai 200092 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

This paper is to study the convergence and superconvergence.of rectangular finite elements under anisotropic meshes. By using of the orthogonal expansion method, an anisotropic Lagrange interpolation is presented. The family of Lagrange rectangular elements with all the possible shape function spaces are considered, which cover the Intermediate families, Tensor-product families and Serendipity families. It is shown that the anisotropic interpolation error estimates hold for any order Sobolev norm. We extend the convergence and superconvergence.result of rectangular finite elements to arbitrary rectangular meshes in a unified way.

关键词： Lagrange interpolation Anisotropic error bounds Arbitrary rectangular meshes,Orthogonal expansion superconvergence.

LOCAL superconvergence.OF CONTINUOUS GALERKIN SOLUTIONS FOR DELAY DIFFERENTIAL EQUATIONS OF PANTOGRAPH TYPE

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Journal of Computational Mathematics 2016年第2期34卷 186-199页

作者： Xiuxiu Xu Qiumei Huang Hongtao Chen Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124 China School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Xiamen 361005 China

This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence.of continuous Galerkin solutions under uniform meshes and locate all the superconvergent points based on the supercloseness between the continuous Galerkin solution U and the interpolation Hhu of the exact solution u. The theoretical results are illustrated by numerical examples.

关键词： Pantograph delay differential equations Uniform mesh Continuous Galerkinmethods Supercloseness superconvergence.

superconvergence.and asymptotic expansions for linear finite element approximations on criss-cross mesh

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Science China Mathematics 2004年第z1期47卷 136-145页

作者： HUANG Yunqing SHU Shi YU Haiyuan Department of Mathematics Xiangtan University Xiangtan 411105 China Department of Mathematics Xiangtan University Xiangtan 411105 China Department of Mathematics Xiangtan University Xiangtan 411105 China

In this paper, we discuss the error estimation of the linear finite element solution on criss-cross mesh. Using space orthogonal decomposition techniques, we obtain an asymptotic expansion and superconvergence.results of the finite element solution. We first prove that the asymptotic expansion has different forms on the two kinds of nodes and then derive a high accuracy combination formula of the approximate derivatives.

关键词： criss-cross mesh, linear finite element, superconvergence.

superconvergence.OF THE MORTAR FINITE ELEMENT APPROXIMATION TO A PARABOLIC PROBLEM

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Systems Science and Mathematical Sciences 1999年第4期12卷 350-356页

作者： GU Hong ZHOU Aihui(Institute of Systems Science, Academia Sinica, Beijing 100080, China) 中科院系统科学所北京 100080

In this paper, a superconvergence.in the mortar finite element approximationfor a elliptic problem has been carried over to a parabolic problem. Both the standardsemidiscrete and the Crank-Nicolson schemes are discussed.

关键词： Mortar finite element parabolic problem superconvergence.

A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection

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Advances in Applied Mathematics and Mechanics 2024年第1期16卷 1-23页

作者： Minqiang Xu Qingsong Zou College of Science Zhejiang University of TechnologyHangzhouZhejiang 310023China School of Computer Science and Engineering Sun Yat-Sen UniversityGuangzhouGuangdong 510275China School of Computer Science and Engineering and Guangdong Province Key Laboratory of Computational ScienceSun Yat-Sen UniversityGuangzhouGuangdong 510275China

In this paper,we present a Hessian recovery based linear finite element method to simulate the molecular beam epitaxy growth model with slope *** the time discretization,we apply a first-order convex splitting method and secondorder Crank-Nicolson *** the space discretization,we utilize the Hessian recovery operator to approximate second-order derivatives of a C^(0)linear finite element function and hence the weak formulation of the fourth-order differential operator can be discretized in the linear finite element *** energy-decay property of our proposed fully discrete schemes is rigorously *** robustness and the optimal-order convergence of the proposed algorithm are numerically *** a large spatial domain for a long period,we simulate coarsening dynamics,where 1/3-power-law is observed.

关键词： Molecular beam epitaxy Hessian recovery linear finite element method superconvergence.

APPLICATION OF superconvergence.TO A MODEL FOR COMPRESSIBLE MISCIBLE DISPLACEMENT

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Numerical Mathematics A Journal of Chinese Universities(English Series) 1998年第1期7卷 25-37页

作者：陈艳萍

A modification of a finite element method of Douglas and Roberts for approximating the solution of the equations describing compressible miscible displacement in a porous medium is proposed and analyzed. The pressure is treated by a parabolic mixed finite element method using a Raviart-Thomas space of index rover a quasiregular partition, An extension of the Darcy velocity along Gauss lines is used in the evaluation of the coefficients in the Galerkin procedure for the concentration. A simple computational procedure allows the superconvergence.property of the fluid velocity to be retained in our total algorithm.

关键词： Compnessible miscible displacement nonlinear system mixed finite element method superconvergence.