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RECOVERY BASED FINITE ELEMENT METHOD FOR biharmonic equation IN 2D

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Journal of Computational Mathematics 2020年第1期38卷 84-102页

作者： Yunqing Huang Huayi Wei Wei Yang Nianyu Yi Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China

We design and numerically validate a recovery based linear finite element method for solving the biharmonic *** main idea is to replace the gradient operator▽on linear finite element space by G(▽)in the weak formulation of the biharmonic equation,where G is the recovery operator which recovers the piecewise constant function into the linear finite element *** operator G,Laplace operator△is replaced by▽·G(▽).Furthermore,the boundary condition on normal derivative▽u-n is treated by the boundary penalty *** explicit matrix expression of the proposed method is also *** examples on the uniform and adaptive meshes are presented to illustrate the correctness and effectiveness of the proposed method.

关键词： biharmonic equation Linear finite element Recovery Adaptive

LOCAL A PRIORI AND A POSTERIORI ERROR ESTIMATE OF TQC9 ELEMENT FOR THE biharmonic equation

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Journal of Computational Mathematics 2008年第2期26卷 196-208页

作者： Ming Wang Weimeng Zhang LMAM School of Mathematical Sciences Peking University Beijing 100871 China Graduate School The Chinese Academy of Social Sciences Beijing 100102 China

In this paper, local a priori, local a posteriori and global a posteriori error estimates are obtained for TQC9 element for the biharmonic equation. An adaptive algorithm is given based on the a posteriori error estim... 详细信息

关键词： Finite element biharmonic equation Apriori error estimate Aposteriori error estimate TQC9 element

CONVERGENCE AND SUPERCONVERGENCE OF HERMITE BICUBIC ELEMENT FOR EIGENVALUE PROBLEM OF THE biharmonic equation

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Journal of Computational Mathematics 2001年第2期19卷 139-142页

作者： Dong-sheng Wu (Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China ) 中科院系统科学所北京 100080

Provides information on a study which discussed the convergence and superconvergence for eigenvalue problem of the biharmonic equation using the Hermite bicubic element. Discussion on eigenvalue problem for biharmonic equation; Background on asymptotic error expansions and interpolation postprocessing; Superconvergence approximations to the eigenvalue and eigenfunction.

关键词： Hermite bicubic element biharmonic equation interpolation postprocessing eigenvalue problem

Multiple Solutions of a Nonlinear biharmonic equation on Graphs

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Communications in Mathematics and Statistics 2023年第4期11卷 767-774页

作者： Songbo Hou Department of Applied Mathematics College of ScienceChina Agricultural UniversityBeijing 100083People’s Republic of China

In this paper,we consider a biharmonic equation with respect to the Dirichlet problem on a domain of a locally finite *** the variation method,we prove that the equation has two distinct solutions under certain condit... 详细信息

关键词： Locallyﬁnite graph biharmonic equation Distinct solutions Mathematics Subject Classiﬁcation 35A15 35G30

OPTIMAL SOLVER FOR MORLEY ELEMENT DISCRETIZATION OF biharmonic equation ON SHAPE-REGULAR GRIDS

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Journal of Computational Mathematics 2016年第2期34卷 159-173页

作者： Chunsheng Feng Shuo Zhang School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China LSEC ICMSEC and NCMIS Academy of Mathematics and System Science Chinese Academy of Sciences Beijing 100190 China

This paper presents an optimal solver for the Morley element problem for the boundaryvalue problem of the biharmonic equation by decomposing it into several subproblems and solving these subproblems optimally. The opt... 详细信息

关键词： biharmonic equation Morley element Optimal solver Precondition Exactsequence.

Accuracy Analysis of the Adini Element for biharmonic equation

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Acta Mathematica Sinica,English Series 2004年第1期20卷 135-146页

作者： PingLUO QunLIN DepartmentofComputerScience TsinghuaUniversityBeijing100084P.R.China AcademyofMathematicsandSystemSciences.ChineseAcademyofSciences Beijing100080P.R.china

In this paper, we consider the solution of the biharmonic equation using Adini nonconforming finite element, and report new results of the asymptotic error expansions of the interpolation error functionals and nonconforming remainder. These expansions are used to develop two extrapolation formulas and a series of sharp error estimates. Finally, the numerical results have verified the extrapolation theory.

关键词： Adini nonconforming element Extrapolation Error expansion biharmonic equation

NONTRIVIAL SOLUTION FOR A CLASS OF SEMILINEAR biharmonic equation INVOLVING CRITICAL EXPONENTS

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Acta Mathematica Scientia 2007年第3期27卷 509-514页

作者：姚仰新王荣鑫沈尧天 School of Mathematical Sciences South China University of Technology

In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequal... 详细信息

关键词： biharmonic equation critical exponent singular term nontrivial solution,Sobolev-Hardy inequality

Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation

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Applied Mathematics and Mechanics(English Edition) 2009年第9期30卷 1177-1182页

作者：尚月强何银年 Faculty of Science Xi'an Jiaotong University School of Mathematics and Computer Science Guizhou Normal University

Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.

关键词： domain decomposition algorithm Schwarz method Fourier transform biharmonic equation

Iterative Method for Solving a Problem with Mixed Boundary Conditions for biharmonic equation

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Advances in Applied Mathematics and Mechanics 2009年第5期1卷 683-698页

作者： Dang Quang A Le Tung Son Institute of Information Technology 18 Hoang Quoc Viet Cau giayHanoiVietnam Pedagogic College Thai Nguyen UniversityVietnam

The solution of boundary value problems(BVP)for fourth order differential equations by their reduction to BVP for second order equations,with the aim to use the available efficient algorithms for the latter ones,attracts attention from many *** this paper,using the technique developed by the authors in recent works we construct iterative method for a problem with complicated mixed boundary conditions for biharmonic equation which is originated from nanofluidic *** convergence rate of the method is proved and some numerical experiments are performed for testing its dependence on a parameter appearing in boundary conditions and on the position of the point where a transmission of boundary conditions occurs.

关键词： Iterative method biharmonic equation mixed boundary conditions