A Priori Error Estimates of Mixed Finite Element Methods for General Linear Hyperbolic Convex Optimal Control Problems

Abstract

The aim of this work is to investigate the discretization of general linear hyperbolic convex optimal control problems by using the mixed finite element methods. The state and costate are approximated by the $k$ order ($k\ge 0$) Raviart-Thomas mixed finite elements and the control is approximated by piecewise polynomials of order $k$. By applying the elliptic projection operators and Gronwall’s lemma, we derive a priori error estimates of optimal order for both the coupled state and the control approximation.