A posteriori error analysis for a distributed optimal control problem governed by the von K\'{a}rm\'{a}n equations

TL;DR

This paper develops and validates a posteriori error estimates for a distributed optimal control problem governed by von Kármán equations, using Morley finite element discretization and piecewise constant controls.

Contribution

It introduces new a posteriori error estimates for the control, state, and adjoint variables in this complex PDE setting, with efficiency analysis and numerical validation.

Findings

A posteriori error estimates are derived and proven to be efficient.

Numerical experiments confirm the theoretical error bounds.

The method effectively guides adaptive refinement for the control problem.

Abstract

This article discusses numerical analysis of the distributed optimal control problem governed by the von K\'{a}rm\'{a}n 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.