Error estimates and superconvergence of mixed finite element methods for fourth order hyperbolic control problems

Abstract

In this paper, we investigate the error estimates and superconvergence of the semidiscrete mixed finite element methods for quadratic optimal control problems governed by linear fourth order hyperbolic equations. The state and the co-state are discretized by the order k Raviart–Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order k(k⩾0). We derive error estimates for both the state and the control approximation. Moreover, we present the superconvergence analysis for mixed finite element approximation of the optimal control problems.