A finite element method for degenerate two-phase flow in porous media. I. Well-posedness
type: Item
instance of: scholarly article
title: A finite element method for degenerate two-phase flow in porous media. I. Well-posedness
zbMATH Open document ID: 1482.65181
author: V. Girault
author: Loic Cappanera
author: Beatrice Riviere
published in: Journal of Numerical Mathematics
publication date: 2021-09-10T00:00:00Z
review text: In this work, a finite element method to solve the immiscible two-phase flow problem in porous media, is formulated. It is known that the preferred unknowns in industrial reservoir simulators are the phase pressure and saturation. The proposed method approximates these unknowns, directly. The discrete saturation satisfies a maximum principle. The numerical method employs mass lumping for integration and an upwind flux technique. Existence of the numerical solutions and some stability bounds are proved. It is also shown that the numerical saturation is bounded between zero and one.
reviewed by: Kanakadurga Sivakumar
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 76T06
Mathematics Subject Classification ID: 76T10
zbMATH DE Number: 7394125
zbMATH Keywords: stability
zbMATH Keywords: compactness
zbMATH Keywords: maximum principle
zbMATH Keywords: pressure-saturation
MaRDI profile type: Publication
full work available at URL: jnma-2020-0004
OpenAlex ID: W3122859288
cites work: Q3747976
cites work: The existence of weak solutions to single porosity and simple dual-porosity models of two-phase incompressible flow
cites work: A Nonlinear Mixed Finite Element Method for a Degenerate Parabolic Equation Arising in Flow in Porous Media
cites work: A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure
cites work: Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in \(L^1\)
cites work: Q4116216
cites work: Q3740471
cites work: Degenerate two-phase incompressible flow. I. Existence, uniqueness and regularity of a weak solution
cites work: Mathematical Analysis for Reservoir Models
cites work: Degenerate two-phase incompressible flow. III: Sharp error estimates.
cites work: Q5185568
cites work: Finite Difference Methods for Two-Phase Incompressible Flow in Porous Media
cites work: Analysis of \(hp\) discontinuous Galerkin methods for incompressible two-phase flow
cites work: Mathematical study of a petroleum-engineering scheme
cites work: A combined finite volume-nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems
cites work: Finite volume methods
cites work: A Control Volume Finite Element Approach to NAPL Groundwater Contamination
cites work: A finite element method for degenerate two-phase flow in porous media. II: Convergence
cites work: Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems
cites work: Flow of oil and water in a porous medium
cites work: A Finite Volume Scheme for Two-Phase Immiscible Flow in Porous Media
cites work: Q4370680
cites work: Analysis of Expanded Mixed Finite Element Methods for a Nonlinear Parabolic Equation Modeling Flow into Variably Saturated Porous Media
cites work: Q4370681
DOI: 10.1515/JNMA-2020-0004
description: scientific article; zbMATH DE number 7394125