Petrov-Galerkin Crank-Nicolson Scheme for Parabolic Optimal Control Problems on Nonsmooth Domains

摘要: In this paper we transfer the a priori error analysis for discretization of parabolic optimal control problems on domains allowing H 2 regularity (i.e. either with smooth boundary or polygonal and convex) to large class nonsmooth domains. We show that combination two ingredients convergence rates respect spatial temporal is required. First need time scheme which has desired rate in case. Secondly method treat singularities due non-smoothness domain corresponding elliptic state equation. particular demonstrate philosophy Crank-Nicolson finite elements suitably graded meshes discretization. A numerical example illustrates predicted rates.