A Mixed Nite Element Discretization on Non-matching Multiblock Grids for a Degenerate Parabolic Equation Arising in Porous Media Ow

| Mixed nite element methods on multiblock domains are considered for nonlinear degenerate parabolic equations arising in modeling multiphase ow in porous media. The subdomain grids need not match on the interfaces, where mortar nite element spaces are introduced to properly impose ux-matching conditions. The low regularity of the solution is treated through time integration, and the degeneracy of the diiusion is handled analitically via the Kirchhoo 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. Multiblock nite elementtechniques on non-matching grids have become increasingly popular in recent years. They combine the exibility of modeling irregularly shaped domains with the convenience of constructing the grids locally. In porous media applications they also allow accurate modeling of large scale geological features such as faults, layers, and fractures. We deene a multiblock domain to be a simply connected domain 2 R d , d = 2 or 3, that is a union of non-overlapping subdomains or blocks i , i = 1; :::; k. For the purpose of the analysis we assume that each block i is convex. In the numerical modeling of multiphase ow in porous media the coupled nonlinear system of conservation equations is often written as an equation of elliptic or parabolic type for some reference pressure and several saturation equations of advection-diiusion type 7, 13]. The diiusion in the saturation equations is degenerate (is zero at extreme saturation values). This causes a very low regularity of the solution and imposes diiculties for the numerical method. In this paper we study mixed nite element discretizations for the saturation equation on multiblock domains. The local mass conservation property of the mixed methods is particularly important in modeling porous media ow. We allow the subdomain grids to be non-matching along the interfaces. To properly impose ux-matching conditions we