We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the multiscale finite element method is similar to the performance of standard finite element methods for smooth problems and present corroborating numerical results.

翻译：本文针对状态方程具有粗糙系数的点式控制约束椭圆分布最优控制问题，构建并分析了一种多尺度有限元方法。我们证明该多尺度有限元方法的性能与标准有限元方法处理光滑问题时的性能相当，并给出了相应的数值验证结果。