Heterogeneous Multiscale Method for elliptic problem without scale separation

TL;DR

This paper demonstrates that the Heterogeneous Multiscale Method can effectively solve elliptic problems lacking scale separation, broadening its applicability beyond traditional assumptions.

Contribution

It extends the Heterogeneous Multiscale Method to elliptic problems without the need for scale separation, including the Localized Orthogonal Method as a special case.

Findings

Applicable to elliptic problems without scale separation

Includes the Localized Orthogonal Method as a special case

Broadens the scope of multiscale methods

Abstract

This paper shows that the Heterogeneous Multiscale Method can be applied to elliptic problem without scale separation. The Localized Orthogonal Method is a special case of the Heterogeneous Multiscale Method.