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Volume 13, Issue 1
A Priori Error Analysis of Mixed Virtual Element Methods for Optimal Control Problems Governed by Darcy Equation

Xiuhe Wang, Qiming Wang & Zhaojie Zhou

DOI: 10.4208/eajam.070322.210722

East Asian J. Appl. Math., 13 (2023), pp. 140-161.

Published online: 2023-01

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  • Abstract

A mixed virtual element discretization of optimal control problems governed by the Darcy equation with pointwise control constraint is investigated. A discrete scheme uses virtual element approximations of the state equation and a variational discretization of the control variable. A discrete first-order optimality system is obtained by the first-discretize-then-optimize approach. A priori error estimates of the state, adjoint, and control variables are derived. Numerical experiments confirm the theoretical results.

  • Keywords

A priori error estimate, mixed virtual element method, optimal control problem.

  • AMS Subject Headings

65N30, 49J20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-13-140, author = {Wang , XiuheWang , Qiming and Zhou , Zhaojie}, title = {A Priori Error Analysis of Mixed Virtual Element Methods for Optimal Control Problems Governed by Darcy Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2023}, volume = {13}, number = {1}, pages = {140--161}, abstract = {

A mixed virtual element discretization of optimal control problems governed by the Darcy equation with pointwise control constraint is investigated. A discrete scheme uses virtual element approximations of the state equation and a variational discretization of the control variable. A discrete first-order optimality system is obtained by the first-discretize-then-optimize approach. A priori error estimates of the state, adjoint, and control variables are derived. Numerical experiments confirm the theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.070322.210722}, url = {http://global-sci.org/intro/article_detail/eajam/21306.html} }
TY - JOUR T1 - A Priori Error Analysis of Mixed Virtual Element Methods for Optimal Control Problems Governed by Darcy Equation AU - Wang , Xiuhe AU - Wang , Qiming AU - Zhou , Zhaojie JO - East Asian Journal on Applied Mathematics VL - 1 SP - 140 EP - 161 PY - 2023 DA - 2023/01 SN - 13 DO - http://doi.org/10.4208/eajam.070322.210722 UR - https://global-sci.org/intro/article_detail/eajam/21306.html KW - A priori error estimate, mixed virtual element method, optimal control problem. AB -

A mixed virtual element discretization of optimal control problems governed by the Darcy equation with pointwise control constraint is investigated. A discrete scheme uses virtual element approximations of the state equation and a variational discretization of the control variable. A discrete first-order optimality system is obtained by the first-discretize-then-optimize approach. A priori error estimates of the state, adjoint, and control variables are derived. Numerical experiments confirm the theoretical results.

Xiuhe Wang, Qiming Wang & Zhaojie Zhou. (2023). A Priori Error Analysis of Mixed Virtual Element Methods for Optimal Control Problems Governed by Darcy Equation. East Asian Journal on Applied Mathematics. 13 (1). 140-161. doi:10.4208/eajam.070322.210722
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