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Degenerate Two-Phase Incompressible Flow IV: Local Refinement and Domain Decomposition

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Southern Methodist University, Box 156, Dallas, Texas, 75275-0156

    Z. Chen

  2. Institute for Scientific Computation, Texas A&M University, College Station, Texas, 77843-3404

    R. E. Ewing

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  1. Z. Chen
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  2. R. E. Ewing
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Chen, Z., Ewing, R.E. Degenerate Two-Phase Incompressible Flow IV: Local Refinement and Domain Decomposition. Journal of Scientific Computing 18, 329–360 (2003). https://doi.org/10.1023/A:1022673427893

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