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 L2 and H1 norm are derived. The
theoretical findings are illustrated by the numerical experiments.
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