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

@article{Coudière2010,
abstract = { 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 h, assuming only the W2,p (for p>2) regularity of the continuous solution, on a mesh of quadrangles. The proof is based on an extension of the ideas developed in [12]. Some new difficulties arise here, due to the weak regularity of the solution, and the necessity to approximate the entire gradient, and not only its normal component, as in [12]. },
author = {Coudière, Yves, Vila, Jean-Paul, Villedieu, Philippe},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite volumes; convection diffusion; convergence rate; unstructured meshes.; finite volume schemes; linear convection-diffusion problem; convergence; unstructured meshes; upwind scheme; diamond cell method; error estimate},
language = {eng},
month = {3},
number = {3},
pages = {493-516},
publisher = {EDP Sciences},
title = {Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem},
url = {http://eudml.org/doc/197561},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Coudière, Yves
AU - Vila, Jean-Paul
AU - Villedieu, Philippe
TI - Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 3
SP - 493
EP - 516
AB - 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 h, assuming only the W2,p (for p>2) regularity of the continuous solution, on a mesh of quadrangles. The proof is based on an extension of the ideas developed in [12]. Some new difficulties arise here, due to the weak regularity of the solution, and the necessity to approximate the entire gradient, and not only its normal component, as in [12].
LA - eng
KW - Finite volumes; convection diffusion; convergence rate; unstructured meshes.; finite volume schemes; linear convection-diffusion problem; convergence; unstructured meshes; upwind scheme; diamond cell method; error estimate
UR - http://eudml.org/doc/197561
ER -