椭圆界面最优控制问题的有限元后验误差估计

A posterior error estimates of the finite element method for elliptic interface optimal control problems

对一类带界面的椭圆最优控制问题给出了有限元逼近格式,其中网格剖分不需要匹配界面。对问题的状态变量和伴随变量用线性连续函数离散,控制变量采用变分离散的方法逼近,最后给出相应的后验误差。

We study a finite element approximation scheme for a class of elliptic optimal control problems with interfaces, where the meshes do not need to fit the interfaces. The state and adjoint state are discretized by continuous piecewise linear functions, and the control variable is approximated by variational discretization. The posterior error estimates are derived.