English

Convergence of a finite element method for degenerate two-phase flow in porous media

Numerical Analysis 2020-01-27 v1 Numerical Analysis

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 the wetting phase pressure and saturation, which are the primary unknowns. The discrete saturation satisfies a maximum principle. Theoretical convergence is proved via a compactness argument. The proof is convoluted because of the degeneracy of the phase mobilities and the unboundedness of the capillary pressure.

Keywords

Cite

@article{arxiv.2001.08859,
  title  = {Convergence of a finite element method for degenerate two-phase flow in porous media},
  author = {Girault Vivette and Riviere Beatrice and Cappanera Loic},
  journal= {arXiv preprint arXiv:2001.08859},
  year   = {2020}
}