This article provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty discontinuous Galerkin method. The main proofs are based on the improved $L^2$-error estimates for the obstacle problem, the discrete maximum principle, and a well-known quadratic growth property. The standard (restrictive) assumptions on mesh are not assumed here.

翻译：本文针对椭圆障碍问题约束下的最优控制问题，建立了基于对称内罚不连续伽辽金方法进行有限元离散的拟最优先验误差估计。主要证明基于障碍问题的改进$L^2$误差估计、离散最大值原理以及经典的二次增长性质。本文未采用标准（限制性）网格假设条件。