We investigate discontinuous Galerkin methods for an elliptic optimal control problem with a general state equation and pointwise state constraints on general polygonal domains. We show that discontinuous Galerkin methods for general second-order elliptic boundary value problems can be used to solve the elliptic optimal control problems with pointwise state constraints. We establish concrete error estimates and numerical experiments are shown to support the theoretical results.

翻译：本文研究具有一般状态方程和逐点状态约束的椭圆最优控制问题在一般多边形域上的间断伽辽金方法。我们证明，针对一般二阶椭圆边值问题的间断伽辽金方法可用于求解带逐点状态约束的椭圆最优控制问题。建立了具体的误差估计，并通过数值实验验证了理论结果。