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Volume 27, Issue 2-3
Variational Discretization for Optimal Control Governed by Convection Dominated Diffusion Equations

Michael Hinze, Ningning Yan & Zhaojie Zhou

J. Comp. Math., 27 (2009), pp. 237-253.

Published online: 2009-04

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  • Abstract

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.

  • Keywords

Constrained optimal control problem, Convection dominated diffusion equation, Edge stabilization Galerkin method, Variational discretization, A priori error estimate, A posteriori error estimate.

  • AMS Subject Headings

65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-27-237, author = {Michael Hinze, Ningning Yan and Zhaojie Zhou}, title = {Variational Discretization for Optimal Control Governed by Convection Dominated Diffusion Equations}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {2-3}, pages = {237--253}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8570.html} }
TY - JOUR T1 - Variational Discretization for Optimal Control Governed by Convection Dominated Diffusion Equations AU - Michael Hinze, Ningning Yan & Zhaojie Zhou JO - Journal of Computational Mathematics VL - 2-3 SP - 237 EP - 253 PY - 2009 DA - 2009/04 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8570.html KW - Constrained optimal control problem, Convection dominated diffusion equation, Edge stabilization Galerkin method, Variational discretization, A priori error estimate, A posteriori error estimate. AB -

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.

Michael Hinze, Ningning Yan and Zhaojie Zhou. (2009). Variational Discretization for Optimal Control Governed by Convection Dominated Diffusion Equations. Journal of Computational Mathematics. 27 (2-3). 237-253. doi:
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