A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem

In this paper, a virtual element method (VEM) discretization of elliptic optimal control problem with pointwise control constraint is investigated. Virtual element discrete scheme is constructed based on virtual element approximation of the state equation and variational discretization of the control variable. A priori error estimates for state, adjoint state and control variable in H-1 and L-2 norms are derived. Due to the attractive flexibility of VEM in dealing with mesh refinement we also derive a posteriori error estimates for the optimal control problem, which are used to guide the mesh refinement in the adaptive VEM algorithm. Numerical experiments are carried out to illustrate the theoretical findings.