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A finite element method for degenerate two-phase flow in porous media. Part I: Well-posedness

  • Vivette Girault , Beatrice Riviere EMAIL logo and Loic Cappanera

Abstract

A finite element method with mass-lumping and flux upwinding is formulated for solving the immiscible two-phase flow problem in porous media. The method approximates directly thewetting phase pressure and saturation, which are the primary unknowns. The discrete saturation satisfies a maximum principle. Stability of the scheme and existence of a solution are established.

JEL Classification: 65M60; 65M12
  1. Funding: The work of the second author was supported in part by NSF-DMS 1913291.

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Received: 2020-01-24
Revised: 2020-07-27
Accepted: 2020-12-23
Published Online: 2021-07-03
Published in Print: 2021-06-25

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