Mathematical study of a petroleum-engineering scheme

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A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities (2018, methodology): “In this respect, we refer to [23, 35] for Galerkin finite elements, to [22, 37, 33] for finite volumes, to [19, 15, 16] for methods combining Galerkin finite elements combined with the mixed finite element method (MFEM), and to [20, 47] for the discontinuous Galerkin method.”
Two-phase flow equations with outflow boundary conditions in the hydrophobic–hydrophilic case (2010, background): “[16] contains also a maximum principle for standard boundary conditions.”
Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equation (2014, methodology): “The standard finite volume scheme (based on a phase-byphase upstream weighting), used in the petroleum engineering framework, was proven to converge in [15]; in this latter work, the estimates on the approximate solutions are obtained thanks to the two-point flux approximation.”
Vertex Approximate Gradient Scheme for Hybrid Dimensional Two-Phase Darcy Flows in Fractured Porous Media (2014, background): “In [12] the convergence is obtained for the usual phase pressures and saturations formulation using a phase by phase upwinding of the mobilities.”
Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure (2013, unknown): “35K65, 35R05, 65M12, 76M12”