Fully Discrete Interpolation Coefficients Mixed Finite Element Methods for Semi-Linear Parabolic Optimal Control Problem

Abstract

We use the fully discrete interpolation coefficient mixed finite element methods to solve the semi-linear parabolic optimal control problems. The space discretization of the state variable is separated using interpolation coefficient mixed finite elements. We approximate the state and the co-state by Raviart-Thomas mixed finite elements on the lowest order, which is approximated by piecewise constant elements. By applying mixed finite element methods to estimate errors, we get priori errors estimates for both the coupled state and the control approximations. We finally confirm the theoretical results numerically by a numerical example.