A posteriori error analysis for a distributed optimal control problem governed by the von Kármán equations

Abstract

This article discusses the numerical analysis of the distributed optimal control problem governed by the von Kármán equations defined on a polygonal domain in ℝ2. The state and adjoint variables are discretised using the nonconforming Morley finite element method and the control is discretized using piecewise constant functions. A priori and a posteriori error estimates are derived for the state, adjoint and control variables. The a posteriori error estimates are shown to be efficient. Numerical results that confirm the theoretical estimates are presented.