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Degenerate two-phase incompressible flow. IV: Local refinement and domain decomposition. (English) Zbl 1032.76590

[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.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76T30 Three or more component flows
76S05 Flows in porous media; filtration; seepage

Citations:

Zbl 1097.76064
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