A finite element method for degenerate two-phase flow in porous media. Part II: Convergence - Archive ouverte HAL Access content directly
Journal Articles Journal of Numerical Mathematics Year : 2021

A finite element method for degenerate two-phase flow in porous media. Part II: Convergence

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Abstract

Convergence of 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. Well-posedness is obtained in [J. Numer. Math., 29(2), 2021]. Theoretical convergence is proved via a compactness argument. The numerical phase saturation converges strongly to a weak solution in L 2 in space and in time whereas the numerical phase pressures converge strongly to weak solutions in L 2 in space almost everywhere in time. The proof is not straightforward because of the degeneracy of the phase mobilities and the unboundedness of the derivative of the capillary pressure.
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Dates and versions

hal-03876363 , version 1 (28-11-2022)

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Vivette Girault, Beatrice Riviere, Loic Cappanera. A finite element method for degenerate two-phase flow in porous media. Part II: Convergence. Journal of Numerical Mathematics, 2021, 29, pp.187-219. ⟨10.1515/jnma-2020-0005⟩. ⟨hal-03876363⟩
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