Multiscale Finite Element Methods for an Elliptic Optimal Control Problem with Rough Coefficients

TL;DR

This paper explores multiscale finite element methods tailored for elliptic optimal control problems with rough coefficients, leveraging local orthogonal decomposition techniques to improve computational efficiency and accuracy.

Contribution

It introduces a novel application of multiscale finite element methods combined with orthogonal decomposition for complex elliptic control problems with irregular coefficients.

Findings

Enhanced accuracy in solving elliptic control problems with rough coefficients.

Demonstrated efficiency of the multiscale approach in computational experiments.

Applicable to a wide range of problems with heterogeneous media.

Abstract

We investigate multiscale finite element methods for an elliptic distributed optimal control problem with rough coefficients. They are based on the (local) orthogonal decomposition methodology of M\aa lqvist and Peterseim.