53 citations · 53 across the 6 of their papers we have counts for
7 papers
The omnidirectional trace in H 1 ()
Robert Eymard, Thierry Gallouët, David Maltese +1
We first prove that all the functions in L 2 whose directional derivative is in L 2 have a directional trace on the boundary of any open bounded domain, without assumptions on its…
Convergence of a Control Volume Finite Element scheme for a cross-diffusion system modeling ion transport
Arne Berrens, Robert Eymard
An approximation of a system coupling the cross-diffusion of chemical species within a solvent, subjected to an electric field, is obtained through a control volume finite element…
Trace operator on H 1 () for general open bounded domains
Robert Eymard, Thierry Gallouët, David Maltese +1
In the case of any bounded open set R d with boundary , we first construct a directional trace in any direction of the unit sphere, for any u L…
Optimal error bounds for the two point flux approximation finite volume scheme
Robert Eymard, Thierry Gallouët, Raphaele Herbin
We consider a finite volume scheme with two-point flux approximation (TPFA) to approximate a Laplace problem when the solution exhibits no more regularity than belonging to $H^1_0(…
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…
Numerical approximation of a reaction-diffusion system with fast reversible reaction
R. Eymard, D. Hilhorst, M. Olech
We consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. We deduce from a priori estimates that the approximate solution converges…
Convergence analysis of a colocated finite volume scheme for the incompressible Navier-Stokes equations on general 2 or 3D meshes
Robert Eymard, Raphaele Herbin, Jean-Claude Latché
We study a colocated cell centered finite volume method for the approximation of the incompressible Navier-Stokes equations posed on a 2D or 3D finite domain. The discrete unknowns…