Virtual element method for semilinear elliptic Neumann boundary optimal control problem.

In this paper, we investigate virtual element discretization of a semilinear elliptic optimal control problem with pointwise Neumann boundary control constraint. The virtual element discrete scheme is constructed based on virtual element discretization of the state equation and variational discretization of the control variable. By utilizing first-order and second-order optimality conditions along with auxiliary problems, we derive a priori error estimates for the state, adjoint state, and control variable in H 1 and L 2 norms. Theoretical results are confirmed by numerical examples. [ABSTRACT FROM AUTHOR]