A finite element method for elliptic optimal control problem on a non-convex polygon with corner singularities

Abstract

In this paper, we study a finite element method overcoming corner singularities for elliptic optimal control problem posed on a polygon. Based on a corner singularity decomposition of singular solution for the associated elliptic system, we derive an extraction formula for coefficients of singular parts, called stress intensity factors, and introduce a finite element discretization for regular parts of the solution pair. Furthermore, we analyze the finite element solutions in L2 and H1 norms. By numerical experiments, we confirm the efficiency and reliability of the proposed method.