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

Abstract

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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].

How to cite

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Coudière, 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 -

Citations in EuDML Documents

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  1. Jérôme Droniou, Thierry Gallouët, Finite volume methods for convection-diffusion equations with right-hand side in H - 1
  2. Olga Drblíková, Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing
  3. Stašová, Olga, Mikula, Karol, Handlovičová, Angela, Peyriéras, Nadine, Nonlinear Tensor Diffusion in Image Processing
  4. Jérôme Droniou, Thierry Gallouët, Finite volume methods for convection-diffusion equations with right-hand side in
  5. Robert Eymard, Cindy Guichard, Raphaèle Herbin, Small-stencil 3D schemes for diffusive flows in porous media
  6. Yves Coudière, Thierry Gallouët, Raphaèle Herbin, Discrete Sobolev inequalities and L p error estimates for finite volume solutions of convection diffusion equations
  7. Robert Eymard, Cindy Guichard, Raphaèle Herbin, Small-stencil 3D schemes for diffusive flows in porous media
  8. Yves Coudière, Thierry Gallouët, Raphaèle Herbin, Discrete Sobolev inequalities and error estimates for finite volume solutions of convection diffusion equations
  9. Yves Coudière, Philippe Villedieu, Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
  10. Komla Domelevo, Pascal Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids

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