“…Starting from these schemes, considerable efforts have been devoted in development of numerical algorithms customized to solve elliptic and parabolic problems with nonmatching grids. The mixed finite element methods (MFEM) [10] have shown some benefits in dealing with nonmatching grid as compared against traditional finite element methods (FEM) (see [11,25,42,8]), and possess good property in local mass-conservation. Nonmatching grids are also adopted in Discontinuous Galerkin (DG) finite element methods, and widely used in the area of multi-scale problems [17,4,12].…”