Superconvergence for Optimal Control Problem Governed by Nonlinear Elliptic Equations

Chang, Yanzhen; Yang, Dinghui

doi:10.1080/01630563.2013.871866

Cited by 2 publications

(3 citation statements)

References 15 publications

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“…where OED .2/ n .2:n,:/ denotes the .n 1/ .n C 1/ matrix, which is obtained by removing the first and last rows of D .2/ n . From the last two equations, we conclude By substituting (21) in the constraint (5b), we have…”

Section: Discretization Of the Constraints From (20) We Havementioning

confidence: 99%

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Direct pseudo-spectral method for optimal control of obstacle problem - an optimal control problem governed by elliptic variational inequality

Oshagh

Shamsi

2017

Math. Meth. Appl. Sci.

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In this paper, a computational technique based on the pseudo‐spectral method is presented for the solution of the optimal control problem constrained with elliptic variational inequality. In fact, our aim in this paper is to present a direct approach for this class of optimal control problems. By using the pseudo‐spectral method, the infinite dimensional mathematical programming with equilibrium constraint, which can be an equivalent form of the considered problem, is converted to a finite dimensional mathematical programming with complementarity constraint. Then, the finite dimensional problem can be solved by the well‐developed methods. Finally, numerical examples are presented to show the validity and efficiency of the technique. Copyright © 2017 John Wiley & Sons, Ltd.

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Section: Discretization Of the Constraints From (20) We Havementioning

confidence: 99%

“…They have implemented some various types of adaptive mesh refinement and proved posteriori error estimate for their approaches. Furthermore, in , the superconvergence of finite element approximation for optimal control problem governed by nonlinear elliptic equations was investigated.…”

Section: Introductionmentioning

confidence: 99%

Direct pseudo-spectral method for optimal control of obstacle problem - an optimal control problem governed by elliptic variational inequality

Oshagh

Shamsi

2017

Math. Meth. Appl. Sci.

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“…Numerical methods for second-order optimal control problems governed by Dirichlet BC have been studied in various articles (see, e.g., [5,10,28,33,34] for distributed control, [2,32] for boundary control, and references therein). For conforming and mixed finite element methods, superconvergence result of control has been derived in [11,12,34].…”

Section: Introductionmentioning

confidence: 99%

The Gradient Discretization Method for Optimal Control Problems, with Superconvergence for Nonconforming Finite Elements and Mixed-Hybrid Mimetic Finite Differences

Droniou¹,

Nataraj²,

Shylaja³

2017

SIAM J. Control Optim.

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In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality system of the control problem. Error estimates for state, adjoint and control variables are derived. Superconvergence results for gradient schemes under realistic regularity assumptions on the exact solution is discussed. These super-convergence results are shown to apply to non-conforming P 1 finite elements, and to the mixed/hybrid mimetic finite differences. Results of numerical experiments are demonstrated for the conforming, non-conforming and mixed-hybrid mimetic finite difference schemes.

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Superconvergence for Optimal Control Problem Governed by Nonlinear Elliptic Equations

Cited by 2 publications

References 15 publications

Direct pseudo-spectral method for optimal control of obstacle problem - an optimal control problem governed by elliptic variational inequality

Direct pseudo-spectral method for optimal control of obstacle problem - an optimal control problem governed by elliptic variational inequality

The Gradient Discretization Method for Optimal Control Problems, with Superconvergence for Nonconforming Finite Elements and Mixed-Hybrid Mimetic Finite Differences

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