Finite volume methods for convection-diffusion equations with right-hand side in
Jérôme Droniou; Thierry Gallouët
- Volume: 36, Issue: 4, page 705-724
- ISSN: 0764-583X
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topDroniou, Jérôme, and Gallouët, Thierry. "Finite volume methods for convection-diffusion equations with right-hand side in $H^{-1}$." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.4 (2002): 705-724. <http://eudml.org/doc/244973>.
@article{Droniou2002,
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 - Modélisation Mathématique et Analyse Numérique},
keywords = {finite volumes; convection-diffusion equations; noncoercivity; non-regular data; finite volume method; convergence; linear elliptic problem},
language = {eng},
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/244973},
volume = {36},
year = {2002},
}
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 - Modélisation Mathématique et Analyse Numérique
PY - 2002
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; convergence; linear elliptic problem
UR - http://eudml.org/doc/244973
ER -
References
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- [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). Zbl1052.65553MR1766855
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