Numerical Methods for Constrained Elliptic Optimal Control Problems with Rapidly Oscillating Coefficients

Abstract

In this paper we use two numerical methods to solve constrained optimal control problems governed by elliptic equations with rapidly oscillating coefficients: one is finite element method and the other is multiscale finite element method. We derive the convergence analysis for those two methods. Analytical results show that finite element method can not work when the parameter $\varepsilon$ is small enough, while multiscale finite element method is useful for any parameter $\varepsilon$.