Finite volume methods for convection-diffusion equations with right-hand side in H-1

Jérôme Droniou; Thierry Gallouët

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 36, Issue: 4, page 705-724
  • ISSN: 0764-583X

Abstract

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We prove the convergence of a finite volume method for a noncoercive linear elliptic problem, with right-hand side in the dual space of the natural energy space of the problem.

How to cite

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Droniou, Jérôme, and Gallouët, Thierry. "Finite volume methods for convection-diffusion equations with right-hand side in H-1." ESAIM: Mathematical Modelling and Numerical Analysis 36.4 (2010): 705-724. <http://eudml.org/doc/194122>.

@article{Droniou2010,
abstract = { We prove the convergence of a finite volume method for a noncoercive linear elliptic problem, with right-hand side in the dual space of the natural energy space of the problem. },
author = {Droniou, Jérôme, Gallouët, Thierry},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite volumes; convection-diffusion equations; noncoercivity; non-regular data.; finite volume method; non-regular data; convergence; linear elliptic problem},
language = {eng},
month = {3},
number = {4},
pages = {705-724},
publisher = {EDP Sciences},
title = {Finite volume methods for convection-diffusion equations with right-hand side in H-1},
url = {http://eudml.org/doc/194122},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Droniou, Jérôme
AU - Gallouët, Thierry
TI - Finite volume methods for convection-diffusion equations with right-hand side in H-1
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 4
SP - 705
EP - 724
AB - We prove the convergence of a finite volume method for a noncoercive linear elliptic problem, with right-hand side in the dual space of the natural energy space of the problem.
LA - eng
KW - Finite volumes; convection-diffusion equations; noncoercivity; non-regular data.; finite volume method; non-regular data; convergence; linear elliptic problem
UR - http://eudml.org/doc/194122
ER -

References

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  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975).  
  2. Y. Coudière, J.P. Vila and P. Villedieu, Convergence rate of a finite volume scheme for a two dimensional convection diffusion problem. ESAIM: M2AN33 (1999) 493-516.  
  3. J. Droniou, Non-coercive linear elliptic problems. Potential Anal.17 (2002) 181-203.  
  4. J. Droniou, Ph.D. thesis, CMI, Université de Provence.  
  5. R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods, in Handbook of Numerical Analysis, Vol. VII, P.G. Ciarlet and J.L. Lions Eds., North-Holland, Amsterdam (1991) 713-1020.  
  6. R. Eymard, T. Gallouët and R. Herbin, Convergence of finite volume approximations to the solutions of semilinear convection diffusion reaction equations. Numer. Math.82 (1999) 91-116.  
  7. J.M. Fiard and R. Herbin, Comparison between finite volume finite element methods for the numerical simulation of an elliptic problem arising in electrochemical engineering. Comput. Methods Appl. Mech. Engrg.115 (1994) 315-338.  
  8. P.A. Forsyth and P.H. Sammon, Quadratic convergence for cell-centered grids. Appl. Numer. Math.4 (1988) 377-394.  
  9. T. Gallouët, R. Herbin and M.H. Vignal, Error estimate for the approximate finite volume solutions of convection diffusion equations with Dirichlet, Neumann or Fourier boundary conditions. SIAM J. Numer. Anal. (2000).  

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