A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods

TL;DR

This paper introduces a multiscale hybrid discontinuous Galerkin method that combines localized orthogonal decomposition with skeletal formulations to efficiently solve elliptic problems with oscillatory coefficients.

Contribution

It is the first to merge hybrid skeletal formulations with localized orthogonal decomposition, enhancing multiscale elliptic problem solutions.

Findings

The method effectively captures fine-scale information at a coarse scale.

Numerical experiments validate the theoretical analysis.

The approach improves computational efficiency for multiscale problems.

Abstract

We formulate and analyze a multiscale method for an elliptic problem with an oscillatory coefficient based on a skeletal (hybrid) formulation. More precisely, we employ hybrid discontinuous Galerkin approaches and combine them with the localized orthogonal decomposition methodology to obtain a coarse-scale skeletal method that effectively includes fine-scale information. This work is the first step in reliably merging hybrid skeletal formulations and localized orthogonal decomposition to unite the advantages of both strategies. Numerical experiments are presented to illustrate the theoretical findings.