Mixed virtual element approximation of a fourth order optimal control problem

In this article, we study mixed virtual element methods for a distributed optimal control problem governed by a fourth order partial differential equation. By introducing an auxiliary variable, the fourth order equation can be transformed into systems of second order equations. A mixed virtual element discrete scheme for the optimal control problem is established. Moreover, a priori error estimates for auxiliary, state, adjoint state and control variable in $H^1$ and $L_2$ norms are derived. Finally, the theoretical finding is verified by numerical experiments.