A Multiscale Finite Element Method for an Elliptic Distributed Optimal Control Problem with Rough Coefficients and Control Constraints

TL;DR

This paper develops a multiscale finite element method tailored for elliptic distributed optimal control problems with rough coefficients and control constraints, demonstrating comparable performance to standard methods for smooth problems.

Contribution

The paper introduces a novel multiscale finite element approach specifically designed for elliptic optimal control problems with rough coefficients and control constraints.

Findings

Method achieves accuracy similar to standard finite element methods for smooth problems.

Numerical results validate the effectiveness of the proposed multiscale approach.

Performance remains robust despite rough coefficients in the state equation.

Abstract

We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the multiscale finite element method is similar to the performance of standard finite element methods for smooth problems and present corroborating numerical results.