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

Abstract

This article discusses numerical analysis of the distributed optimal control problem governed by the von Kármán equations defined on a polygonal domain in ${\mathbb{R}}^2$. 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.

23 pages, 3 figures, 4 tables