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ON THE ERROR ESTIMATE OF LINEAR finite element approximation TO THE ELASTIC CONTACT PROBLEM WITH CURVED CONTACT BOUNDARY

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Journal of Computational Mathematics 2000年第6期18卷 561-566页

作者： Lie-heng Wang (State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

In this paper, the linear finite element approximation to the elastic contact problem with curved contact boundary is considered. The error bound O(h[sup ?]) is obtained with requirements of two times continuously differentiable for contact boundary and the usual regular triangulation, while *** et. al. Obtained the error bound O(h[sup ?]) with requirements of three times continuously differentiable for contact boundary and extra regularities of triangulation (c.f. [2]). [ABSTRACT FROM AUTHOR]

关键词： contact problem finite element approximation

ADAPTIVE finite element approximation FOR A CLASS OF PARAMETER ESTIMATION PROBLEMS

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Journal of Computational Mathematics 2010年第5期28卷 645-675页

作者： Karl Kunisch Wenbin Liu Yanzhen Chang Ningning Yan Ruo Li Department of Mathematics University of Graz Austria KBS University of Kent Canterbury CT2 7NF England LSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Computational Mathematics Peking University China

In this paper, we study adaptive finite element discretisation schemes for a class of parameter estimation problem. We propose to efficient algorithms for the estimation problem use adaptive multi-meshes in developing We derive equivalent a posteriori error estimators for both the state and the control approximation, which particularly suit an adaptive multi-mesh finite element scheme. The error estimators are then implemented and tested with promising numerical results.

关键词： Parameter estimation finite element approximation Adaptive finite elementmethods A posteriori error estimate.

THE approximationS OF THE EXACT BOUNDARY CONDITION AT AN ARTIFICIAL BOUNDARY FOR LINEARIZED INCOMPRESSIBLE VISCOUS FLOWS

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Journal of Computational Mathematics 1998年第3期16卷 239-256页

作者： Wei-zhu Bao (Department of Applied Mathematics, Tsinghua University, Beijing 100084, P.R. China) 清华大学应用数学系北京

We consider the linearized incompressible Navier-Stokes (Oseen) equations in a flat channel. A sequence of approximations to the exact boundary condition at an artificial boundary is derived. Then the original problem is reduced to a boundary value problem in a bounded domain, which is well-posed. A finite element approximation on the bounded domain is given, furthermore the error estimate of the finite element approximation is obtained. Numerical example shows that our artificial boundary conditions are very effective.

关键词： Oseen equations artificial boundary artificial boundary condition finite element approximation error estimate

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.

A PRIORI ERROR ESTIMATE AND SUPERCONVERGENCE ANALYSIS FOR AN OPTIMAL CONTROL PROBLEM OF BILINEAR TYPE

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Journal of Computational Mathematics 2008年第4期26卷 471-487页

作者： Danping Yang Yanzhen Chang Wenbin Liu Department of Mathematics East China Normal University Shanghai 200062 China School of Mathematics and System Science Shandong University Jinan 250100 China KBS University of Kent Canterbury CT2 7PE England

In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L^2-norm error estimates and the almost optimal L^∞-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.

关键词： Bilinear control problem finite element approximation Superconvergence Apriori error estimate A posteriori error estimator.

A finite element ALGORITHM FOR NEMATIC LIQUID CRYSTAL FLOW BASED ON THE GAUGE-UZAWA METHOD

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Journal of Computational Mathematics 2022年第1期40卷 26-43页

作者： Pengzhan Huang Yinnian He Ting Li College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830046China School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an 710049China

In this paper,we present a finite element algorithm for the time-dependent nematic liquid crystal flow based on the Gauge-Uzawa *** algorithm combines the Gauge and Uzawa methods within a finite element variational formulation,which is a fully discrete projection type algorithm,whereas many projection methods have been studied without space ***,error estimates for velocity and molecular orientation of the nematic liquid crystal flow are ***,numerical results are given to show that the presented algorithm is reliable and confirm the theoretical analysis.

关键词： Nematic liquid crystal model finite element approximation Gauge-Uzawa method Error analysis

RECOVERY A POSTERIORI ERROR ESTIMATES FOR GENERAL CONVEX ELLIPTIC OPTIMAL CONTROL PROBLEMS SUBJECT TO POINTWISE CONTROL CONSTRAINTS

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Journal of Computational Mathematics 2009年第4期27卷 543-560页

作者： Yanping Chen Yao Fu Huanwen Liu Yongquan Dai Huayi Wei School of Mathematical Sciences South China Normal University Guangzhou 510631 China College of Mechanical Engineering Jiangxi Yu Zhou Scientific and Technological Institute Xinyu 338029 China School of Mathematics and Computer Science Guangxi University for Nationalities Nanning 530006 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University

Superconvergence and recovery a posteriori error estimates of the finite element ap- proximation for general convex optimal control problems are investigated in this paper. We obtain the superconvergence properties of finite element solutions, and by using the superconvergence results we get recovery a posteriori error estimates which are asymptotically exact under some regularity conditions. Some numerical examples are provided to verify the theoretical results.

关键词： General convex optimal control problems finite element approximation Control constraints Superconvergence Recovery operator.

CONVERGENCE OF AN ALTERNATING A-φ SCHEME FOR QUASI-MAGNETOSTATIC EDDY CURRENT PROBLEM

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Journal of Computational Mathematics 2004年第5期22卷 661-670页

作者： Chang-fengMa DepartmentofMathematics HuazhongUniversityofScienceandTechnologyWuhan430074China

We propose in this paper an alternating A-φ method for the quasi-magnetostatic eddy current problem by means of finite element approximations. Bounds for continuous and discrete error in finite time are given. And it is verified that provided the time step τ is sufficiently small, the proposed algorithm yields for finite time T an error of O(h+τ^1/2) in the L^2-norm for the magnetic field H(=μ^-1△↓×A), where h is the mesh size, μ the magnetic permeability.

关键词： Eddy current problem Alternating A-φ method finite element approximation Error estimates

approximation of thermoelasticity contact problem with nonmonotone friction

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Applied Mathematics and Mechanics(English Edition) 2010年第1期31卷 77-86页

作者： Ivan ESTAK Boko S. JOVANOVI Faculty of Mine and Geology University of Belgrade Faculty of Mathematics University of Belgrade

The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a nonmonotone and multivalued law. The coupling effect of the problem is neglected. Therefore, the thermic part of the problem is considered independently on the elasticity problem. For the displacement vector, we formulate one substationary problem for a non-convex, locally Lipschitz continuous functional representing the total potential energy of the body. All problems formulated in the paper are approximated with the finite element method.

关键词： static thermoelastic contact nonmonotone multivalued friction hemivari-ational inequality substationary problem finite element approximation