Flux-Mortar Mixed Finite Element Methods on NonMatching Grids

We investigate a mortar technique for mixed finite element approximations of class domain decomposition saddle point problems on nonmatching grids in which the variable associated with essential boundary condition, referred to as flux, is chosen coupling variable. It plays role Lagrange multiplier impose weakly continuity natural condition. The flux-mortar incorporated use discrete extension operator. present well-posedness and error analysis an abstract setting under set suitable assumptions, followed by nonoverlapping algorithm that reduces global problem positive definite interface problem. theory illustrated Darcy flow, where normal flux used pressure, Stokes velocity vector stress. In both examples, operators are developed assumptions from verified. Numerical studies illustrating theoretical results presented flow.