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Standard and Economical Cascadic Multigrid Methods for the Mortar Finite Element Methods 被引量:3
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作者 Xuejun Xu Wenbin Chen 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2009年第2期180-201,共22页
In this paper, standard and economical cascadic multigrid methods are considered for solving the algebraic systems resulting from the mortar finite element methods. Both cascadic multigrid methods do not need full ell... In this paper, standard and economical cascadic multigrid methods are considered for solving the algebraic systems resulting from the mortar finite element methods. Both cascadic multigrid methods do not need full elliptic regularity, so they can be used to tackle more general elliptic problems. Numerical experiments are reported to suonort our theorv. 展开更多
关键词 cascadic multigrid mortar finite elements.
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CASCADIC MULTIGRID METHODS FOR MORTAR WILSON FINITE ELEMENT METHODS ON PLANAR LINEAR ELASTICITY
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作者 陈文斌 汪艳秋 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2003年第1期1-18,共18页
Cascadic multigrid technique for mortar Wilson finite element method ofhomogeneous boundary value planar linear elasticity is described and analyzed. Firstthe mortar Wilson finite element method for planar linear elas... Cascadic multigrid technique for mortar Wilson finite element method ofhomogeneous boundary value planar linear elasticity is described and analyzed. Firstthe mortar Wilson finite element method for planar linear elasticity will be analyzed,and the error estimate under L2 and H1 norm is optimal. Then a cascadic multigridmethod for the mortar finite element discrete problem is described. Suitable grid trans-fer operator and smoother are developed which lead to an optimal cascadic multigridmethod. Finally, the computational results are presented. 展开更多
关键词 平面线性弹性 研钵威尔逊有限元法 多栅技术 弹性力学
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A Cascadic Multigrid Algorithm for the Mortar Element Method for Semiliner Ellptic Problems
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作者 邹战勇 《嘉应学院学报》 2015年第11期5-10,共6页
In this paper a cascadic multigrid algorithm for the mortar finite element approximation of the semilinear elliptic problem is proposed,and corresponding theorems aregiven,which display the error estimate and the comp... In this paper a cascadic multigrid algorithm for the mortar finite element approximation of the semilinear elliptic problem is proposed,and corresponding theorems aregiven,which display the error estimate and the computational complexity of the method. 展开更多
关键词 Mortar finite element cascadic multigrid method Senilinear elliptic problems
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An Adaptive Least-Squares Mixed Finite Element Method for Fourth Order Parabolic Problems
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作者 Ning Chen Haiming Gu 《Applied Mathematics》 2013年第4期675-679,共5页
A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approxi... A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved. 展开更多
关键词 ADAPTIVE METHOD LEAST-SQUARES Mixed finite element METHOD FOURTH Order parabolic problems LEAST-SQUARES Functional A POSTERIORI Error
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Asymptotic expansions of finite element solutions to Robin problems in H^3 and their application in extrapolation cascadic multigrid method 被引量:1
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作者 HU HongLing CHEN ChuanMiao PAN KeJia 《Science China Mathematics》 SCIE 2014年第4期687-698,共12页
For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the... For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented. 展开更多
关键词 finite element Richardson extrapolation Robin problem asymptotic expansion cascadic multi-grid method
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L^2-ERROR OF EXTRAPOLATION CASCADIC MULTIGRID (EXCMG) 被引量:1
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作者 陈传淼 胡宏伶 +1 位作者 谢资清 李郴良 《Acta Mathematica Scientia》 SCIE CSCD 2009年第3期539-551,共13页
Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method (EXCMG) is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial val... Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method (EXCMG) is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG. 展开更多
关键词 cascadic multigrid finite element new extrapolation quadratic interpolation L^2-error
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Uniform Convergence of Multigrid V-Cycle on Adaptively Refined Finite Element Meshes for Elliptic Problems with Discontinuous Coefficients
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作者 Haijun Wu Weiying Zheng 《Communications in Mathematical Research》 CSCD 2023年第3期437-475,共39页
The multigrid V-cycle methods for adaptive finite element discretizations of two-dimensional elliptic problems with discontinuous coefficients are considered.Under the conditions that the coefficient is quasi-monotone... The multigrid V-cycle methods for adaptive finite element discretizations of two-dimensional elliptic problems with discontinuous coefficients are considered.Under the conditions that the coefficient is quasi-monotone up to a constant and the meshes are locally refined by using the newest vertex bisection algorithm,some uniform convergence results are proved for the standard multigrid V-cycle algorithm with Gauss-Seidel relaxations performed only on new nodes and their immediate neighbours.The multigrid V-cycle algorithm uses O(N)operations per iteration and is optimal. 展开更多
关键词 multigrid adaptive finite elements elliptic problems discontinuous coefficients uniform convergence
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A MODIFIED WEAK GALERKIN FINITE ELEMENTMETHOD FOR SINGULARLY PERTURBED PARABOLIC CONVECTION-DIFFUSION-REACTION PROBLEMS
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作者 Suayip Toprakseven Fuzheng Gao 《Journal of Computational Mathematics》 SCIE CSCD 2023年第6期1246-1280,共35页
In this work,a modified weak Galerkin finite element method is proposed for solving second order linear parabolic singularly perturbed convection-diffusion equations.The key feature of the proposed method is to replac... In this work,a modified weak Galerkin finite element method is proposed for solving second order linear parabolic singularly perturbed convection-diffusion equations.The key feature of the proposed method is to replace the classical gradient and divergence operators by the modified weak gradient and modified divergence operators,respectively.We apply the backward finite difference method in time and the modified weak Galerkin finite element method in space on uniform mesh.The stability analyses are presented for both semi-discrete and fully-discrete modified weak Galerkin finite element methods.Optimal order of convergences are obtained in suitable norms.We have achieved the same accuracy with the weak Galerkin method while the degrees of freedom are reduced in our method.Various numerical examples are presented to support the theoretical results.It is theoretically and numerically shown that the method is quite stable. 展开更多
关键词 The modified weak Galerkin finite element method Backward Euler method parabolic convection-diffusion problems Error estimates
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P1-NONCONFORMING QUADRILATERAL FINITE VOLUME ELEMENT METHOD AND ITS CASCADIC MULTIGRID ALGORITHM FOR ELLIPTIC PROBLEMS 被引量:3
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作者 Hong-ying Man Zhong-ci Shi 《Journal of Computational Mathematics》 SCIE EI CSCD 2006年第1期59-80,共22页
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 mu... 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. 展开更多
关键词 finite volume element method cascadic multigrid Elliptic problems
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MULTIGRID FOR THE MORTAR FINITE ELEMENT FOR PARABOLIC PROBLEM 被引量:6
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作者 Xue-junXu Jin-ruChen 《Journal of Computational Mathematics》 SCIE EI CSCD 2003年第4期411-420,共10页
In this paper, a mortar finite element method for parabolic problem is presented. Multi-grid method is used for solving the resulting discrete system. It is shown that the multigrid method is optimal, i.e, the converg... In this paper, a mortar finite element method for parabolic problem is presented. Multi-grid method is used for solving the resulting discrete system. It is shown that the multigrid method is optimal, i.e, the convergence rate is independent of the mesh size L and the time step parameter τ. 展开更多
关键词 multigrid Mortar element parabolic problem.
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CASCADIC MULTIGRID FOR PARABOLIC PROBLEMS CASCADIC MULTIGRID FOR PARABOLIC PROBLEMS 被引量:18
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作者 Zhong-ci Shi, Xue-jun Xu (State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China) 《Journal of Computational Mathematics》 SCIE CSCD 2000年第5期551-560,共10页
In this paper, we develop the cascadic multigrid method for parabolic problems. The optimal convergence accuracy and computation complexity are obtained.
关键词 cascadic multigrid finite element parabolic problem.
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Cascadic multigrid methods for parabolic problems 被引量:7
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作者 DU Qiang MING PingBing 《Science China Mathematics》 SCIE 2008年第8期1415-1439,共25页
In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is establishe... In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the smoother.Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular smoothers.Optimal error bound sare derived for both smooth and non-smooth data.Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented. 展开更多
关键词 cascadic multigrid method parabolic problem finite element methods backward Euler scheme smoother STABILITY optimal error order optimal complexity 65N30 65N55 65F10
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Superconvergence analysis of fully discrete finite element methods for semilinear parabolic optimal control problems 被引量:3
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作者 Yuelong TANG Yanping CHEN 《Frontiers of Mathematics in China》 SCIE CSCD 2013年第2期443-464,共22页
We study the superconvergence property of fully discrete finite element approximation for quadratic optimal control problems governed by semilinear parabolic equations with control constraints. The time discretization... We study the superconvergence property of fully discrete finite element approximation for quadratic optimal control problems governed by semilinear parabolic equations with control constraints. The time discretization is based on difference methods, whereas the space discretization is done using finite element methods. The state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant functions. First, we define a fully discrete finite element approximation scheme for the semilinear parabolic control problem. Second, we derive the superconvergence properties for the control, the state and the adjoint state. Finally, we do some numerical experiments for illustrating our theoretical results. 展开更多
关键词 Superconvergence property quadratic optimal control problem fully discrete finite element approximation semilinear parabolic equation interpolate operator
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Fully Discrete H^(1) -Galerkin Mixed Finite Element Methods for Parabolic Optimal Control Problems 被引量:1
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作者 Tianliang Hou Chunmei Liu Hongbo Chen 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2019年第1期134-153,共20页
In this paper,we investigate a priori and a posteriori error estimates of fully discrete H^(1)-Galerkin mixed finite element methods for parabolic optimal control prob-lems.The state variables and co-state variables a... In this paper,we investigate a priori and a posteriori error estimates of fully discrete H^(1)-Galerkin mixed finite element methods for parabolic optimal control prob-lems.The state variables and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element and linear finite element,and the control vari-able is approximated by piecewise constant functions.The time discretization of the state and co-state are based on finite difference methods.First,we derive a priori error estimates for the control variable,the state variables and the adjoint state variables.Second,by use of energy approach,we derive a posteriori error estimates for optimal control problems,assuming that only the underlying mesh is static.A numerical example is presented to verify the theoretical results on a priori error estimates. 展开更多
关键词 parabolic equations optimal control problems a priori error estimates a posteriori error estimates H^(1)-Galerkin mixed finite element methods
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Multi-mesh Adaptive Finite Element Algorithms for Constrained Optimal Control Problems Governed By Semi-Linear Parabolic Equations
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作者 Tie-jun CHEN Jian-xin XIAO Hui-ying WANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2014年第2期411-428,共18页
In this paper, we derive a posteriori error estimators for the constrained optimal control problems governed by semi-linear parabolic equations under some assumptions. Then we use them to construct reliable and effici... In this paper, we derive a posteriori error estimators for the constrained optimal control problems governed by semi-linear parabolic equations under some assumptions. Then we use them to construct reliable and efficient multi-mesh adaptive finite element algorithms for the optimal control problems. Some numerical experiments are presented to illustrate the theoretical results. 展开更多
关键词 semi-linear parabolic equations constrained optimal control problems adaptive finite element methods a posteriori error estimators
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Immersed Finite Element Method for Interface Problems with Algebraic Multigrid Solver
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作者 Wenqiang Feng Xiaoming He +1 位作者 Yanping Lin Xu Zhang 《Communications in Computational Physics》 SCIE 2014年第4期1045-1067,共23页
This article is to discuss the bilinear and linear immersed finite element(IFE)solutions generated from the algebraic multigrid solver for both stationary and moving interface problems.For the numerical methods based ... This article is to discuss the bilinear and linear immersed finite element(IFE)solutions generated from the algebraic multigrid solver for both stationary and moving interface problems.For the numerical methods based on finite difference formulation and a structured mesh independent of the interface,the stiffness matrix of the linear system is usually not symmetric positive-definite,which demands extra efforts to design efficient multigrid methods.On the other hand,the stiffness matrix arising from the IFE methods are naturally symmetric positive-definite.Hence the IFE-AMG algorithm is proposed to solve the linear systems of the bilinear and linear IFE methods for both stationary and moving interface problems.The numerical examples demonstrate the features of the proposed algorithms,including the optimal convergence in both L 2 and semi-H1 norms of the IFE-AMG solutions,the high efficiency with proper choice of the components and parameters of AMG,the influence of the tolerance and the smoother type of AMG on the convergence of the IFE solutions for the interface problems,and the relationship between the cost and the moving interface location. 展开更多
关键词 Interface problems immersed finite elements algebraic multigrid method
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LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS 被引量:7
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作者 Dan-ping Yang (School of Mathematics and System Science, Shandong University, Jinan 250100, China) 《Journal of Computational Mathematics》 SCIE EI CSCD 2002年第2期153-164,共12页
Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Informatio... Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Information on the least-squares mixed element schemes for nonlinear parabolic problem. 展开更多
关键词 least-squares algorithm mixed finite element nonlinear parabolic problems convergence analysis
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A POSTERIORI ERROR ESTIMATES OF FINITEELEMENT METHOD FOR PARABOLIC PROBLEMS 被引量:2
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作者 陈艳萍 《Acta Mathematica Scientia》 SCIE CSCD 1999年第4期449-456,共8页
This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the p... This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context. 展开更多
关键词 Aposteriori error estimates finite element method parabolic problem
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SUPERCONVERGENCE OF THE MORTAR FINITE ELEMENT APPROXIMATION TO A PARABOLIC PROBLEM 被引量:1
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作者 GU Hong ZHOU Aihui(Institute of Systems Science, Academia Sinica, Beijing 100080, China) 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1999年第4期350-356,共7页
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.
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Multigrid Method for Poroelasticity Problem by Finite Element Method 被引量:2
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作者 Luoping Chen Yanping Chen 《Advances in Applied Mathematics and Mechanics》 SCIE 2019年第6期1339-1357,共19页
In this paper,we will investigate a multigrid algorithm for poroelasticity problem by a new finite element method with homogeneous boundary conditions in two dimensional space.We choose N´ed´elec edge elemen... In this paper,we will investigate a multigrid algorithm for poroelasticity problem by a new finite element method with homogeneous boundary conditions in two dimensional space.We choose N´ed´elec edge element for the displacement variable and piecewise continuous polynomials for the pressure variable in the model problem.In constructing multigrid algorithm,a distributive Gauss-Seidel iteration method is applied.Numerical experiments shows that the finite element method achieves optimal convergence order and the multigrid algorithm is almost uniformly convergent to mesh size h and parameter dt on regular meshes. 展开更多
关键词 Poroelasticity problem finite element method multigrid method
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