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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.

FINITE ELEMENT APPROXIMATION FOR A CLASS OF PARAMETER ESTIMATION PROBLEMS

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Journal of Systems Science & Complexity 2014年第5期27卷 866-882页

作者： chang yanzhen YANG Danping Department of Mathematics Beijing University of Chemical Technology Department of Mathematics Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal University

This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant *** authors derive some a priori error estimates for both the control and state ***,the numerical experiments verify the theoretical results.

关键词： A priori error estimate finite element approximation optimal control problems

A POSTERIORI ERROR ESTIMATE OF FINITE ELEMENT METHOD FOR THE OPTIMAL CONTROL WITH THE STATIONARY BENARD PROBLEM

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Journal of Computational Mathematics 2013年第1期31卷 68-87页

作者： yanzhen chang Danping Yang Department of Mathematics Beijing University of Chemical Technology Beijing 100029 China Department of Mathematics East China Normal University Shanghai 200062 China

In this paper, we consider the adaptive finite element approximation for the distributed optimal control associated with the stationary Benard problem under the pointwise control constraint. The states and co-states are approximated by polynomial functions of lowest- order mixed finite element space or piecewise linear functions and control is approximated by piecewise constant functions. We give the a posteriori error estimates for the control, the states and co-states.

关键词： Optimal control problem Stationary Benard problem Nonlinear coupled sys-tem A posteriori error estimate.

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.

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.