Title:         Mortar mixed finite element methods on irregular 
               multiblock domains

Authors:       Ivan Yotov

Source:        IMACS Series in Comp. Appl. Math. vol. 4, 
               Iterative Methods in Scientific Computation,
               J. Wang et al. (1998) 239--244

Status:        Published

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

Keywords:      Mixed finite element, mortar finite element, 
               error estimates, superconvergence, multiblock, 
               non-matching grids