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

DOI10.1515/jnma-2020-0005zbMath1481.65183OpenAlexW3123813362MaRDI QIDQ2665981

Vivette Girault, Loic Cappanera, Béatrice Rivière

Publication date: 22 November 2021

Published in: Journal of Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jnma-2020-0005

zbMATH Keywords

convergenceweak solutiondegenerate coefficientsunbounded capillary pressure

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Weak solutions to PDEs (35D30) Fractional partial differential equations (35R11) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22) Liquid-liquid two component flows (76T06)

Related Items (6)

Upstream mobility finite volumes for the Richards equation in heterogenous domains ⋮ A vertex scheme for two-phase flow in heterogeneous media ⋮ Maximum-principle-satisfying discontinuous Galerkin methods for incompressible two-phase immiscible flow ⋮ An efficient and physically consistent numerical method for the Maxwell–Stefan–Darcy model of two‐phase flow in porous media ⋮ An energy stable, conservative and bounds‐preserving numerical method for thermodynamically consistent modeling of incompressible two‐phase flow in porous media with rock compressibility ⋮ A finite element method for degenerate two-phase flow in porous media. I. Well-posedness

Cites Work

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• A Control Volume Finite Element Approach to NAPL Groundwater Contamination
• Mathematical study of a petroleum-engineering scheme

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