We establish the equivalence between the Multiscale Hybrid-Mixed (MHM) and the Multiscale Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomial source terms. Under the idealized assumption that the local problems defining the multiscale basis functions are exactly solved, we prove that the equivalence holds for general polytopal (coarse) meshes and arbitrary approximation orders. Also, we leverage the interchange of properties to perform a unified convergence analysis, as well as to improve on both methods.

翻译：我们确立了多比例混合混合(MHM)和多比例混合高级命令(MHHHO)方法之间的等值,以便用片断的多元源术语解决可变扩散问题。根据确定多尺度基础函数的本地问题完全解决的理想假设,我们证明普通多端(粗)间衣和任意近似命令的等值。此外,我们利用属性交换来进行统一的趋同分析,并改进这两种方法。