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24

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Introduction

## Publications

Publications (24)

We approximate the solution to some linear and degenerate quasi-linear problem involving a linear elliptic operator (like the semi-discrete in time implicit Euler approximation of Richards and Stefan equations) with measure right-hand side and heterogeneous anisotropic diffusion matrix. This approximation is obtained through the addition of a weigh...

The present paper addresses the convergence of a first order in time incremental projection scheme for the time-dependent incompressible Navier-Stokes equations to a weak solution, without any assumption of existence or regularity assumptions on the exact solution. We prove the convergence of the approximate solutions obtained by the semi-discrete...

We approximate the solution to some linear and degenerate quasi-linear problem involving a linear elliptic operator (like the semi-discrete in time implicit Euler approximation of Richards and Stefan equations) with measure right-hand side and heterogeneous anisotropic diffusion matrix. This approximation is obtained through the addition of a weigh...

We propose a reduced model accounting capillary trapping to simulate oil migration in geological basins made of several rock types. Our model is derived from Darcy type models thanks to Dupuit approximation and a vertical integration in each geological layer. We propose a time-implicit finite volume scheme which is shown to be unconditionally stabl...

We study a sharp interface model in the context of seawater intrusion in an anisotropic unconfined aquifer. It is a degenerate parabolic system with cross‐diffusion modeling the flow of fresh and saltwater. We study a nonlinear control volume finite element scheme. This scheme ensures the nonnegativity of the discrete solution without any restricti...

We prove existence of a solution to the implicit MAC scheme for the compressible Navier–Stokes equations. We derive error estimates for this scheme on two and three dimensional Cartesian grids. Error estimates are obtained by using the discrete version of the relative energy method introduced on the continuous level in Feireisl et al. (J Math Fluid...

We consider a degenerate parabolic system modelling the flow of fresh and saltwater in an anisotropic porous medium in the context of seawater intrusion. We propose and analyze a nonlinear Control Volume Finite Element scheme. This scheme ensures the nonnegativity of the discrete solution without any restriction on the mesh and on the anisotropy te...

We prove in this paper the convergence of the marker and cell (MAC) scheme for the discretization of the steady state compressible and isentropic Navier-Stokes equations on two- or three-dimensional Cartesian grids. Existence of a solution to the scheme is proven, followed by estimates on approximate solutions, which yield the convergence of the ap...

We prove in this paper the convergence of the marker-and-cell (MAC) scheme for the discretization of the semi-stationary compressible Stokes equations on two or three dimensional Cartesian grids. Existence of a solution to the scheme is stated, followed by estimates on approximate solutions, which yields the convergence of the approximate solutions...

We prove in this paper the convergence of the Marker and Cell (MAC) scheme for the discretization of the steady state compressible and isentropic Navier-Stokes equations on two or three-dimensional Cartesian grids. Existence of a solution to the scheme is proven, followed by estimates on approximate solutions, which yield the convergence of the app...

We consider the compressible Navier-Stokes system with variable entropy. The pressure is a nonlinear function of the density and the entropy/potential temperature which, unlike in the Navier-Stokes-Fourier system, satisfies only the transport equation. We provide existence results within three alternative weak formulations of the corresponding clas...

We prove in this paper the convergence of the Marker and Cell (MAC) scheme for the discretization of the steady state compressible and isentropic Navier-Stokes equations on two or three dimensional Cartesian grids.

We consider the compressible Navier-Stokes system with variable entropy. The pressure is a nonlinear function of the density and the entropy/potential temperature which, unlike in the Navier-Stokes-Fourier system, satisfies only the transport equation. We provide existence results within three alternative weak formulations of the corresponding clas...

We derive an a priori error estimate for the numerical solution obtained by
time and space discretization by the finite volume/finite element method of the
barotropic Navier--Stokes equations. The numerical solution on a convenient
polyhedral domain approximating a sufficiently smooth bounded domain is
compared with an exact solution of the barotro...

We present here a general method based on the investigation of the relative energy of the system that provides an unconditional error estimate for the approximate solution of the barotropic Navier-Stokes equations obtained by time and space discretization. We use this methodology to derive an error estimate for a specific DG/finite element scheme f...

We consider the barotropic Navier-Stokes system describing the motion of a compressible viscous fluid confined to a straight layer Ω ε = ω × (0, ε), where ω is a particular 2-D domain (a periodic cell, bounded domain or the whole 2 − D space). We show that the weak solutions in the 3D domain converge to a (strong) solutions of the 2 − D Navier-Stok...

In this paper, we propose a discretization for the nonsteady compressible Stokes Problem. This scheme is based on Crouzeix-Raviart approximation spaces. The discretization of the momentum balance is obtained by the usual finite element technique. The discrete mass balance is obtained by a finite volume scheme, with an upwinding of the density. The...