Some error estimates of finite volume element approximation for elliptic optimal control problems (Q2865636)

Distributed optimal control problems governed by elliptic equations with control constrained are solved using the finite volume element method. The authors make use of the variational discretization approach, where the control variable is not discretized directly, but discretized by a projection of the discrete adjoint variable. The optimal order error estimates for the state, adjoint and control variables are of second order of the mesh size as for the linear finite elements with variational discretization. The theoretical results are confirmed on a numerical test problem.