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

Yves Coudière; Philippe Villedieu

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 6, page 1123-1149
  • ISSN: 0764-583X

Abstract

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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 H1 finite volume space. We actually prove the convergence of the scheme in a discrete H1 norm, with an error estimate of order O(h) (on meshes of size h).

How to cite

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Coudière, Yves, and Villedieu, Philippe. "Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes." ESAIM: Mathematical Modelling and Numerical Analysis 34.6 (2010): 1123-1149. <http://eudml.org/doc/197542>.

@article{Coudière2010,
abstract = { 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 H1 finite volume space. We actually prove the convergence of the scheme in a discrete H1 norm, with an error estimate of order O(h) (on meshes of size h). },
author = {Coudière, Yves, Villedieu, Philippe},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite volumes; mesh refinement; convection-diffusion; convergence rate.; convection-diffusion equation; finite volume method; convergence; error estimate},
language = {eng},
month = {3},
number = {6},
pages = {1123-1149},
publisher = {EDP Sciences},
title = {Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes},
url = {http://eudml.org/doc/197542},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Coudière, Yves
AU - Villedieu, Philippe
TI - Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 6
SP - 1123
EP - 1149
AB - 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 H1 finite volume space. We actually prove the convergence of the scheme in a discrete H1 norm, with an error estimate of order O(h) (on meshes of size h).
LA - eng
KW - Finite volumes; mesh refinement; convection-diffusion; convergence rate.; convection-diffusion equation; finite volume method; convergence; error estimate
UR - http://eudml.org/doc/197542
ER -

References

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