Mortar Mixed Finite Element Methods on Irregular Multiblock Domains

We consider an expanded version of the lowest order Raviart-Thomas mixed nite element method for elliptic equations on irregular multiblock domains. The logically rectangular subdomain grids may not match on the interfaces. Continuous or discontin-uous piece-wise multilinear mortar nite element spaces are introduced on the interfaces to approximate the scalar variable (pressure) and impose ux-matching conditions. The method is further reduced via quadrature rules to cell-centered nite diierences for the subdomain pressures, coupled through the mortars. Under certain subdomain smoothness assumptions, superconvergence for both the pressure and its ux is shown at the cell-centers. A parallel domain decomposition algorithm is used to solve the discrete system by reducing it to a positive deenite problem in the mortar spaces.