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Coupling discontinuous Galerkin and mixed finite element discretizations using mortar finite elements

V. Girault, S. Sun, M. F. Wheeler and I. Yotov, "Coupling discontinuous Galerkin and mixed finite element discretizations using mortar finite elements", SIAM Journal on Numerical Analysis, 46(2), 949–979, 2008.
Vivette Girault, Shuyu Sun, Mary F. Wheeler, and Ivan Yotov
discontinuous Galerkin, mixed finite element, flow in porous media, mortar finite element, interface problem
2008
Discontinuous Galerkin (DG) and mixed finite element (MFE) methods are two popular methods that possess local mass conservation. In this paper we investigate DG-DG and DG-MFE domain decomposition couplings using mortar finite elements to impose weak continuity of fluxes and pressures on the interface. The subdomain grids need not match, and the mortar grid may be much coarser, giving a two-scale method. Convergence results in terms of the fine subdomain scale h and the coarse mortar scale H are established for both types of couplings. In addition, a nonoverlapping parallel domain decomposition algorithm is developed, which reduces the coupled system to an interface mortar problem. The properties of the interface operator are analyzed.