Chen, Z.; Ewing, R. E. Degenerate two-phase incompressible flow. IV: Local refinement and domain decomposition. (English) Zbl 1032.76590 J. Sci. Comput. 18, No. 3, 329-360 (2003). [For part III see the authors, Numer. Math. 90, 215-240 (2001; Zbl 1097.76064).]Summary: This is the fourth paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. In this paper we describe a finite element approximation for this system on locally refined grids. This adaptive approximation is based on a mixed finite element method for the elliptic pressure equation and a Galerkin finite element method for the degenerate parabolic saturation equation. Both discrete stability and sharp a priori error estimates are established for this approximation. Iterative techniques of domain decomposition type for solving it are discussed, and numerical results are presented. Cited in 1 ReviewCited in 4 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76T30 Three or more component flows 76S05 Flows in porous media; filtration; seepage Keywords:Porous media; degenerate elliptic-parabolic system; finite element; stability; error estimate; locally refined grids; domain decomposition Citations:Zbl 1097.76064 PDFBibTeX XMLCite \textit{Z. Chen} and \textit{R. E. Ewing}, J. Sci. Comput. 18, No. 3, 329--360 (2003; Zbl 1032.76590) Full Text: DOI