检索结果-南通市图书馆

Four-Order Superconvergent Weak Galerkin Methods for the biharmonic equation on Triangular Meshes

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications on Applied Mathematics and Computation 2023年第4期5卷 1323-1338页

作者： Xiu Ye Shangyou Zhang Department of Mathematics University of Arkansas at Little RockLittle RockAR72204USA Department of Mathematical Sciences University of DelawareNewarkDE19716USA

A stabilizer-free weak Galerkin(SFWG)finite element method was introduced and analyzed in Ye and Zhang(SIAM J.Numer.Anal.58:2572–2588,2020)for the biharmonic equation,which has an ultra simple finite element formulation.This work is a continuation of our investigation of the SFWG method for the biharmonic equation.The new SFWG method is highly accurate with a convergence rate of four orders higher than the optimal order of convergence in both the energy norm and the L^(2)norm on triangular grids.This new method also keeps the formulation that is symmetric,positive definite,and stabilizer-free.Four-order superconvergence error estimates are proved for the corresponding SFWG finite element solutions in a discrete H^(2)norm.Superconvergence of four orders in the L^(2)norm is also derived for k≥3,where k is the degree of the approximation polynomial.The postprocessing is proved to lift a P_(k)SFWG solution to a P_(k+4)solution elementwise which converges at the optimal order.Numerical examples are tested to verify the theor ies.

关键词： Finite element Weak Hessian Weak Galerkin(WG) biharmonic equation Triangular mesh

A Mixed Finite Element Scheme for biharmonic equation with Variable Coefficient and von Kármán equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Computational Physics 2022年第5期31卷 1434-1466页

作者： Huangxin Chen Amiya K.Pani Weifeng Qiu School of Mathematical Sciences and Fujian Provincial Key Laboratory on MathematicalModeling and High Performance Scientific Computing Xiamen UniversityFujian361005China Department of Mathematics Indian Institute of TechnologyBombayPowaiMumbai-400076India Department of Mathematics City University of Hong Kong83 Tat Chee AvenueKowloonHong KongChina

In this paper,a new mixedfinite element scheme using element-wise stabilization is introduced for the biharmonic equation with variable coefficient on Lipschitz polyhedral domains.The proposed scheme doesn’t involve any integration along mesh interfaces.The gradient of the solution is approximated by H(div)-conforming BDMk+1 element or vector valued Lagrange element with order k+1,while the solution is approximated by Lagrange element with order k+2 for any k≥0.This scheme can be easily implemented and produces symmetric and positive definite linear system.We provide a new discrete H^(2)-norm stability,which is useful not only in analysis of this scheme but also in C^(0) interior penalty methods and DG methods.Optimal convergences in both discrete H^(2)-norm and L^(2)-norm are derived.This scheme with its analysis is further generalized to the von K´arm´an equations.Finally,numerical results verifying the theoretical estimates of the proposed algorithms are also presented.

关键词： biharmonic equation von K´arm´an equations mixedfinite element methods element-wise stabilization discrete H2-stability positive definite

biharmonic equation and an Improved Hardy Inequality

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2004年第3期20卷 433-440页

作者： Yang-xinYao Yao-tianShen Zhi-huiChen DepartmenofAppliedMathematics SouthChinaUniversityofTechnologyGuangzhou510640China

An improved Hardy inequality will be proven in the present work. Using the improved Hardy inequality and variational techniques, we also discuss the existence of nontrivial solution for following the weighted eigenval... 详细信息

关键词： biharmonic equation Hardy inequality nontrivial solution

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

在线全文

学校读者我要写书评

暂无评论

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

在线全文

学校读者我要写书评

暂无评论

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

RECOVERY BASED FINITE ELEMENT METHOD FOR biharmonic equation IN 2D

在线全文

学校读者我要写书评

暂无评论

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 equation.The 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 space.By operator G,Laplace operator△is replaced by▽·G(▽).Furthermore,the boundary condition on normal derivative▽u-n is treated by the boundary penalty method.The explicit matrix expression of the proposed method is also introduced.Numerical 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

Accuracy Analysis of the Adini Element for biharmonic equation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

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

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

在线全文

学校读者我要写书评

暂无评论

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 researchers.In 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 physics.The 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

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

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

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.