A new superconvergence of finite elements for bilinear parabolic optimal control problems

Abstract

In this paper, we consider a fully discrete finite element approximation of bilinear parabolic optimal control problems with an integral constraint. First, we give an approximation scheme of the model problem, where triangular finite element and backward Euler methods are used. Second, we introduce some useful intermediate variables, interpolation operators and related error estimates. Third, we derive a new superconvergence between the numerical solutions and projection functions of exact solutions. Last, a numerical example is provided to verify our results.