A Priori Error Analysis of Mixed Virtual Element Methods for Optimal Control Problems Governed by Darcy Equation
Year: 2023
Author: Xiuhe Wang, Qiming Wang, Zhaojie Zhou
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.070322.210722
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 1 : pp. 140–161
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: A priori error estimate mixed virtual element method optimal control problem.
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