%0 Journal Article
%T Virtual Element Discretization of Optimal Control Problem Governed by Brinkman Equations
%A Yanwei Li
%J Engineering
%P 114-133
%@ 1947-394X
%D 2023
%I Scientific Research Publishing
%R 10.4236/eng.2023.152010
%X In this
paper, we discuss virtual element method (VEM) approximation of optimal control
problem governed by Brinkman equations with control constraints. Based on the
polynomial projections and variational discretization of the control variable,
we build up the virtual element discrete scheme of the optimal control problem
and derive the discrete first order optimality system. A priori error estimates
for the state, adjoint state and control variables in <i>L</i><sup>2</sup> and <i>H</i><sup>1</sup> norm are derived. The
theoretical findings are illustrated by the numerical experiments.
%K Virtual Element Method
%K Optimal Control Problem
%K Brinkman Equations
%K A Priori Error Estimate
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=123251