Currently displaying 1 – 7 of 7

Showing per page

Order by Relevance | Title | Year of publication

Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes

Yves CoudièrePhilippe Villedieu — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We study a finite volume method, used to approximate the solution of the linear two dimensional convection diffusion equation, with mixed Dirichlet and Neumann boundary conditions, on Cartesian meshes refined by an automatic technique (which leads to meshes with hanging nodes). We propose an analysis through a discrete variational approach, in a discrete finite volume space. We actually prove the convergence of the scheme in a discrete norm, with an error estimate...

Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)

Christophe BerthonYves CoudièreVivien Desveaux — 2014

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

We discuss new MUSCL reconstructions to approximate the solutions of hyperbolic systems of conservations laws on 2D unstructured meshes. To address such an issue, we write two MUSCL schemes on two overlapping meshes. A gradient reconstruction procedure is next defined by involving both approximations coming from each MUSCL scheme. This process increases the number of numerical unknowns, but it allows to reconstruct very accurate gradients. Moreover a particular attention is paid on the limitation...

Discrete Sobolev inequalities and L p error estimates for finite volume solutions of convection diffusion equations

Yves CoudièreThierry GallouëtRaphaèle Herbin — 2001

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

The topic of this work is to obtain discrete Sobolev inequalities for piecewise constant functions, and to deduce L p error estimates on the approximate solutions of convection diffusion equations by finite volume schemes.

Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem

Yves CoudièreJean-Paul VilaPhilippe Villedieu — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, a class of cell centered finite volume schemes, on general unstructured meshes, for a linear convection-diffusion problem, is studied. The convection and the diffusion are respectively approximated by means of an upwind scheme and the so called diamond cell method [4]. Our main result is an error estimate of order , assuming only the (for ) regularity of the continuous solution, on a mesh of quadrangles. The proof is based on an extension of the ideas developed in [12]. Some...

Page 1

Download Results (CSV)