Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Inhomogeneous Boundary Value Problems with High Contrast Coefficients

In this article we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for elliptic partial differential equations with inhomogeneous Dirichlet, Neumann, and Robin boundary conditions, high contrast property emerges from coefficients of operators conditions. By careful construction bases CEM-GMsFEM, introduce two which are used to handle Dirichlet Neumann values also proved converge independently ratios as enlarging oversampling regions. We providean a priori error estimate show that number layers is key factor in controlling numerical errors. A series experiments conducted, those results reflect reliability our methods even ratios.