"A Three-Field Domain Decomposition Method" is the title of a seminal paper by F. Brezzi and L. D. Marini which introduces a three-field formulation for elliptic partial differential equations. Based on that, we propose the Multiscale-Hybrid-Hybrid Method (MH$^2$M) for the Darcy model, a multiscale finite element method that yields, after a series of formal manipulations, a symmetric positive definite formulation that depends only on the trace of the solution. We show stability and convergence results for a family of finite element spaces and establish relationships with other multiscale finite element methods.

翻译：《一种三场区域分解方法》是F. Brezzi与L. D. Marini的奠基性论文标题，该文引入了椭圆型偏微分方程的三场公式。在此基础上，我们针对Darcy模型提出了多尺度-混合-混合方法（MH$^2$M），这是一种多尺度有限元方法，经过一系列形式化处理，可得到仅依赖于解迹的对称正定公式。我们展示了一族有限元空间的稳定性与收敛性结果，并建立了与其他多尺度有限元方法之间的联系。