227 citations · 324 across the 17 of their papers we have counts for
22 papers
Optimal error estimates for non-conforming approximations of linear parabolic problems with minimal regularity
J Droniou, R Eymard, T Gallouët +2
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler…
Convergence of the fully discrete incremental projection scheme for incompressible flows
Thierry Gallouët, Raphaèle Herbin, Jean-Claude Latché +1
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,…
A new convergence proof for approximations of the Stefan problem
Robert Eymard, Thierry Gallouët
We consider the Stefan problem, firstly with regular data and secondly with irregular data. In both cases is given a proof for the convergence of an approximation obtained by regul…
Finite volume schemes and Lax-Wendroff consistency
R Eymard, T Gallouët, R Herbin +1
We present a (partial) historical summary of the mathematical analysis of finite differences and finite volumes methods, paying a special attention to the Lax-Richtmyer and Lax-Wen…
Weak Consistency of Finite Volume Schemes for Systems of Non Linear Conservation Laws: Extension to Staggered Schemes
T Gallouët, R Herbin, J. -C Latché
We prove in this paper the weak consistency of a general finite volume convection operator acting on discrete functions which are possibly not piecewise-constant over the cells of…
A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem
Mine Akbas, Thierry Gallouet, Almut Gassmann +2
A novel notion for constructing a well-balanced scheme - a gradient-robust scheme - is introduced and a showcase application for a steady compressible, isothermal Stokes equations…
Consistent Internal Energy Based Schemes for the Compressible Euler Equations
R. Herbin, T. Gallouët, J. -C Latché +1
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to e…
On The Weak Consistency of Finite Volumes Schemes for Conservation Laws on General Meshes
Thierry Gallouët, R. Herbin, J. -C Latché
The aim of this paper is to develop some tools in order to obtain the weak consistency of (in other words, analogues of the Lax-Wendroff theorem for) finite volume schemes for bala…
The gradient discretisation method for linear advection problems
Jérôme Droniou, Robert Eymard, T. Gallouët +1
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equation…
A unified analysis of elliptic problems with various boundary conditions and their approximation
Jérôme Droniou, Robert Eymard, T. Gallouët +1
We design an abstract setting for the approximation in Banach spaces of operators acting in duality. A typical example are the gradient and divergence operators in Lebesgue--Sobole…
Entropy estimates for a class of schemes for the euler equations
Thierry Gallouet, Raphaele Herbin, J. -C Latché +1
In this paper, we derive entropy estimates for a class of schemes for the Euler equations which present the following features: they are based on the internal energy equation (even…
Convergence of the mac scheme for variable density flows
Thierry Gallouët, Raphaele Herbin, Jean-Claude Latché +1
We prove in this paper the convergence of an semi-implicit MAC scheme for the time-dependent variable density Navier-Stokes equations.
Analysis of a fractional-step scheme for the P1 radiative diffusion model
Raphaele Herbin, Thierry Gallouët, Jean-Claude Latché +1
We address in this paper a nonlinear parabolic system, which is built to retain the main mathematical difficulties of the P1 radiative diffusion physical model. We propose a finite…
Convergence of the MAC scheme for the incompressible Navier-Stokes equations
Thierry Gallouët, Raphaele Herbin, J. -C Latché +1
We prove in this paper the convergence of the Marker and cell (MAC) scheme for the dis-cretization of the steady-state and unsteady-state incompressible Navier-Stokes equations in…
Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations
Thierry Gallouet, Raphaele Herbin, Jean-Claude Latché +1
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…
Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations
Thierry Gallouet, Raphaele Herbin, David Maltese +1
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…
Two-phase flows involving capillary barriers in heterogeneous porous media
Clément Cancès, Thierry Gallouet, Alessio Porretta
We consider a simplified model of a two-phase flow through a heterogeneous porous medium, in which the convection is neglected. This leads to a nonlinear degenerate parabolic probl…
Some possibly degenerate elliptic problems with measure data and non linearity on the boundary
Thierry Gallouët, Yannick Sire
The goal of this paper is to study some possibly degenerate elliptic equation in a bounded domain with a nonlinear boundary condition involving measure data. We investigate two typ…
A unified approach to Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite Volume methods
Jerome Droniou, Robert Eymard, Thierry Gallouët +1
We investigate the connections between several recent methods for the discretization of anisotropic heterogeneous diffusion operators on general grids. We prove that the Mimetic Fi…
On the time continuity of entropy solutions
Clément Cancès, Thierry Gallouet
We show that any entropy solution of a convection diffusion equation in $\OT$ belongs to . The proof does not use the un…
Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid interfaces
Robert Eymard, Thierry Gallouët, Raphaele Herbin
A discretisation scheme for heterogeneous anisotropic diffusion problems on general meshes is developed and studied. The unknowns of this scheme are the values at the centre of the…
A cell-centred finite volume approximation for second order partial derivative operators with full matrix on unstructured meshes in any space dimension
Robert Eymard, Thierry Gallouët, Raphaèle Herbin
Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant fu…