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.  Zbl0937.65116
  3. J. Droniou, Non-coercive linear elliptic problems. Potential Anal.17 (2002) 181-203.  Zbl1161.35362
  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.  Zbl0981.65095
  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.  Zbl0930.65118
  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.  Zbl0651.65086
  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).  Zbl1052.65553

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