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

摘要

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 L-2 and H-1 norms. By numerical experiments, we confirm the efficiency and reliability of the proposed method. (C) 2017 Elsevier Ltd. All rights reserved.