Displaying similar documents to “A stabilized mixed finite element method for single-phase compressible flow.”

Mortar finite element discretization of a model coupling Darcy and Stokes equations

Christine Bernardi, Tomás Chacón Rebollo, Frédéric Hecht, Zoubida Mghazli (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where the Darcy and Stokes equations are coupled appropriate matching conditions on the interface. We propose a discretization of this problem which combines the mortar method with standard finite elements, in order to handle separately the flow inside and outside the porous medium. We prove and error estimates for the resulting discrete problem. Some numerical experiments confirm...

A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions

Christine Bernardi, Frédéric Hecht, Rüdiger Verfürth (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a variational formulation of the three-dimensional Navier–Stokes equations with mixed boundary conditions and prove that the variational problem admits a solution provided that the domain satisfies a suitable regularity assumption. Next, we propose a finite element discretization relying on the Galerkin method and establish and error estimates.

Coupling Darcy and Stokes equations for porous media with cracks

Christine Bernardi, Frédéric Hecht, Olivier Pironneau (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization...