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

A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods