Error estimates for the numerical approximation of a distributed optimal control problem governed by the von K\'arm\'an equations

TL;DR

This paper develops and validates error estimates for finite element approximations of a distributed optimal control problem governed by von Karman equations, including control constraints and minimal regularity assumptions.

Contribution

It introduces a priori error estimates for the discretization of state, adjoint, and control variables in von Karman optimal control problems with point-wise constraints.

Findings

Error estimates are derived for all variables involved.

Numerical results confirm the theoretical error bounds.

The approach handles minimal regularity assumptions.

Abstract

In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Karman equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed to discretize the state and adjoint variables. The control is discretized using piece-wise constant approximations. A priori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions on the exact solution. Numerical results that justify the theoretical results are presented.