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 a first step to reliably merge hybrid skeletal formulations and localized orthogonal decomposition and unite the advantages of both strategies. Numerical experiments are presented to illustrate the theoretical findings.

翻译：本文基于骨架（混合）公式，针对具有振荡系数的椭圆问题提出并分析了一种多尺度方法。具体而言，我们采用混合间断伽辽金方法，并结合局部正交分解方法论，以获得一种有效包含精细尺度信息的粗尺度骨架方法。本研究是可靠地融合混合骨架公式与局部正交分解、结合两种策略优势的第一步。文中通过数值实验验证了理论发现。