A Priori Error Analysis of Mixed Virtual Element Methods for Optimal Control Problems Governed by Darcy Equation

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.