Error estimates for a mixed finite element discretization of a two-phase porous media flow model with dynamic capillarity

X. Cao (Corresponding author), K. Mitra

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Abstract

We analyze a fully discrete numerical scheme for the model describing two-phase immiscible flow in porous media with dynamic effects in the capillary pressure. We employ the Euler implicit method for the time discretization. The spatial discretization is based on the mixed finite element method (MFEM). Specifically, the lowest order Raviart–Thomas elements are applied. In this paper, the error estimates for the saturation, fluxes and phase pressures in L (0,T;L 2 (Ω)) are derived for the temporal and spatial discretization to show the convergence of the scheme. Finally, we present some numerical results to support the theoretical findings.

Original languageEnglish
Pages (from-to)164-178
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume353
DOIs
Publication statusPublished - 1 Jun 2019

Fingerprint

Porous Media Flow
Capillarity
Mixed Finite Elements
Finite Element Discretization
Two-phase Flow
Two phase flow
Porous materials
Error Estimates
Discretization
Fluxes
Finite element method
Element Order
Flow in Porous Media
Mixed Finite Element Method
Implicit Method
Time Discretization
Numerical Scheme
Euler
Saturation
Lowest

Keywords

  • Dynamic capillary pressure
  • Euler implicit method
  • Immiscible two-phase flow
  • Mixed finite elements

Cite this

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Error estimates for a mixed finite element discretization of a two-phase porous media flow model with dynamic capillarity. / Cao, X. (Corresponding author); Mitra, K.

In: Journal of Computational and Applied Mathematics, Vol. 353, 01.06.2019, p. 164-178.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Mitra, K.

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AB - We analyze a fully discrete numerical scheme for the model describing two-phase immiscible flow in porous media with dynamic effects in the capillary pressure. We employ the Euler implicit method for the time discretization. The spatial discretization is based on the mixed finite element method (MFEM). Specifically, the lowest order Raviart–Thomas elements are applied. In this paper, the error estimates for the saturation, fluxes and phase pressures in L ∞ (0,T;L 2 (Ω)) are derived for the temporal and spatial discretization to show the convergence of the scheme. Finally, we present some numerical results to support the theoretical findings.

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KW - Euler implicit method

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