Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints

TL;DR

This paper explores finite element methods applied to elliptic distributed optimal control problems with pointwise state constraints, focusing on their formulation and analysis through the lens of fourth order boundary value problems.

Contribution

It introduces a novel finite element approach tailored for elliptic optimal control problems with pointwise constraints, connecting them to fourth order boundary value problems.

Findings

Effective finite element discretization for constrained control problems

Analysis of convergence and stability of the proposed methods

Potential for improved numerical solutions in constrained optimal control

Abstract

Finite element methods for a model elliptic distributed optimal control problem with pointwise state constraints are considered from the perspective of fourth order boundary value problems.