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

Yves Coudière; Jean-Paul Vila; Philippe Villedieu

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 3, page 493-516
- ISSN: 0764-583X

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topCoudière, Yves, Vila, Jean-Paul, and Villedieu, Philippe. "Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem." ESAIM: Mathematical Modelling and Numerical Analysis 33.3 (2010): 493-516. <http://eudml.org/doc/197561>.

@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 -

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