Title:         A mixed finite element discretization on non-matching 
               multiblock grids for a degenerate parabolic equation 
               arising in porous media flow

Authors:       Ivan Yotov

Source:        East-West J. Numer. Math. 5 (1997) 211--230

Status:        Published 

Abstract: Mixed finite element methods on multiblock domains are
considered for nonlinear degenerate parabolic equations arising in
modeling multiphase flow in porous media. The subdomain grids need not
match on the interfaces, where mortar finite element spaces are
introduced to properly impose flux-matching conditions. The low
regularity of the solution is treated through time integration, and
the degeneracy of the diffusion is handled analitically via the
Kirchhoff transformation. With an appropriate choice of the mortar
spaces, the error for both a semidiscrete (continuous time) scheme and
a fully discrete (backward Euler) scheme is bounded entirely by
approximation error terms of optimal order.

Keywords:      Mixed finite element, degenerate parabolic equation, 
               nonlinear, mortar finite element, multiblock,
               non-matching grids, error estimates, porous media

Subj. class.:  65M60, 65M12, 65M15, 35K65, 76S05