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variational discretization FOR OPTIMAL CONTROL GOVERNED BY CONVECTION DOMINATED DIFFUSION EQUATIONS

Journal of Computational Mathematics 2009年第2期27卷 237-253页

作者： Michael Hinze Ningning Yan Zhaojie Zhou Department of Mathematics University of Hamburg Germany LSEC Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Science Beijing 100190 China

In this paper, we study variational discretization for the constrained optimal control problem governed by convection dominated diffusion equations, where the state equation is approximated by the edge stabilization Galerkin method. A priori error estimates are derived for the state, the adjoint state and the control. Moreover, residual type a posteriori error estimates in the L^2-norm are obtained. Finally, two numerical experiments are presented to illustrate the theoretical results.

关键词： Constrained optimal control problem Convection dominated diffusion equation Edge stabilization Galerkin method variational discretization A priori error estimate A posteriori error estimate.

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Error Estimates of variational discretization and Mixed Finite Element Methods for Quasilinear Optimal Control Problems

Error Estimates of Variational Discretization and Mixed Fini...

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第24届中国控制与决策会议

作者： Zuliang Lu 1,2 , Xiao Huang 3 1. School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404000, China 2. College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, China3. College of Electronics and Information Engineering, Chongqing Three Gorges University, Chongqing 404100, China

In this paper we study a variational discretization and mixed finite element approximation of optimal control problems governed by quasilinear elliptic equations. The state and co-state are approximated by the lowest order Raviart- Thomas mixed finite element spaces and the control is not discreted. We derive a priori error estimates both for the state variables and the control variable. Finally, a numerical example is given to demonstrate the theoretical results.

关键词： Error estimates quasilinear optimal control problems variational discretization mixed finite element methods

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A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for Parabolic Optimal Control Problems

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Advances in Applied Mathematics and Mechanics 2013年第5期5卷 688-704页

作者： Xianbing Luo Yanping Chen Yunqing Huang School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105HunanChina School ofMathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina School of Science Guizhou UniversityGuiyang 550025GuizhouChina

In this paper,the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic *** optimal convergent order O(h^(2)+k^(2))is obtained for the ... 详细信息

关键词： variational discretization parabolic optimal control problems finite volume element method distributed control Crank-Nicolson

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A priori error estimates of finite volume element method for hyperbolic optimal control problems

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Science China Mathematics 2013年第5期56卷 901-914页

作者： LUO XianBing CHEN YanPing HUANG YunQing School of Mathematics and Computational Science Xiangtan University School of Science Guizhou University School of Mathematical Sciences South China Normal University

In this paper,optimize-then-discretize,variational discretization and the finite volume method are applied to solve the distributed optimal control problems governed by a second order hyperbolic equation.A semi-discrete optimal system is *** prove the existence and uniqueness of the solution to the semidiscrete optimal system and obtain the optimal order error estimates in L ∞(J;L 2)-and L ∞(J;H 1)-*** experiments are presented to test these theoretical results.

关键词： second order hyperbolic equation optimal control problems finite volume element method dis- tributed control variational discretization

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Finite Volume Element Method for Solving the Elliptic Neumann Boundary Control Problems

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Applied Mathematics 2020年第12期11卷 1243-1252页

作者： Quanxiang Wang College of Science Nanjing Agricultural University Nanjing China

Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method for solving the elliptic Neumann boundary control problems. The variational discretization approach is used to deal with the control. Numerical results demonstrate that the proposed method for control is second-order accuracy in the L2 (Γ) and L∞ (Γ) norm. For state and adjoint state, optimal convergence order in the L2 (Ω) and H1 (Ω) can also be obtained.

关键词： Finite Volume Element Neumann Boundary Control variational discretization

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