Error Estimates of Semidiscrete Mixed Methods for Optimal Control Problems Governed by Parabolic Integro-differential Equations

Abstract

In this paper, we investigate the L ∞(L 2)-error estimates of the semidiscrete mixed finite element methods for quadratic optimal control problems governed by parabolic integro-differential equations. The state and the costate are discretized by the order k Raviart–Thomas mixed finite element spaces, and the control is approximated by piecewise polynomials of order k≥0. We derive error estimates for both the state and the control approximations.