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In this paper, we consider two types of couplings for mixed finite element and weak Galerkin methods for elliptic problems. The first coupling simply connects the subdomain schemes on the interfaces by use of the numerical flux and pressure. The second one is based on a mortar space and imposes the weak continuity of the numerical flux. We derive solvability and a priori error estimates for both couplings. Keywords Couplings Error estimates Mixed finite element Mortar space Non-matching grids Weak Galerkin
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