Domain decomposition and mortar mixed approach for nonlinear elliptic equations modeling flow in porous media.

The equations describe the behavior of steady state flow in porous medium generally results in elliptic partial differential equations with coefficient represents the permeability of the medium. This article presents the extension of mortar mixed method for second order nonlinear elliptic equations that describes flow in porous media. The domain is decomposed into non-overlapping regions with each partitioned independently. The grids on subdomains are allowed to be non-matching across the subdomains internal boundaries. The fixed point argument (FPA) is employed to establish the existence and uniqueness of discrete problem, and optimal order error estimates are provided for approximations. The computational results are given to validate the theory.