In this paper we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of the state variable on the boundary, which reduces the regularity of solutions to the optimal control problems. We construct the mixed virtual element discrete scheme and derive a priori error estimate for the optimal control problem based on the variational discretization for the control variable. Numerical experiments are carried out on different meshes to support our theoretical findings.

翻译：本文研究具有边界观测的椭圆最优控制问题的混合虚拟元逼近。此类最优控制问题的目标泛函包含状态变量在边界上的外法向导数，这降低了最优控制问题解的正则性。我们构建了混合虚拟元离散格式，并基于控制变量的变分离散给出了该最优控制问题的先验误差估计。在不同网格上进行的数值实验验证了我们的理论结果。