A superconvergent scheme for a locking‐free FEM in a Timoshenko optimal control problem

Abstract

AbstractIn this work we analyze the numerical approximation of an optimal control problem of a Timoshenko beam, by considering two kinds of distributed control. The discretization of the control variables is performed by using piecewise constant functions. The states and the adjoint states are approximated by a locking free scheme of linear finite elements. An interpolation postprocessing technique is used for the approximations of the optimal solution of the continuous optimal control problem. It is proved that these approximations have superconvergence order h2, which do not depend on the thickness of the beam.