We present a new error analysis for finite element methods for a linear-quadratic elliptic optimal control problem with Neumann boundary control and pointwise control constraints. It can be applied to standard finite element methods when the coefficient s in the elliptic operator are smooth and also to multiscale finite element methods when the coefficients are rough.

翻译：本文针对带Neumann边界控制及点态控制约束的线性二次椭圆最优控制问题，提出了一种有限元方法的新误差分析。该分析适用于椭圆算子系数光滑时的标准有限元方法，也适用于系数粗糙时的多尺度有限元方法。