Superconvergence of Variational Discretization for Bilinear Elliptic Optimization Problems

Abstract

Abstract-In this paper, variational discretization approximation of bilinear elliptic optimal control problems is considered. Firstly, we construct a variational discretization method for the bilinear elliptic optimal control problem with control constraints. Secondly, we derive the convergence of the approximation scheme. Thirdly, we analyze the superconvergence. Finally, we present a numerical example to conform our theoretical results.