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.

翻译：我们基于骨架（混合）变分形式，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，并将其与局部正交分解技术相结合，从而获得一种能有效包含细尺度信息的粗尺度骨架方法。本研究是可靠融合混合骨架变分形式与局部正交分解方法、以结合两者优势的首步探索。数值实验展示了理论结果的有效性。