# 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

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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 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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- J. Droniou, Non-coercive linear elliptic problems. Potential Anal.17 (2002) 181-203.
- J. Droniou, Ph.D. thesis, CMI, Université de Provence.
- 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.
- 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.
- 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.
- P.A. Forsyth and P.H. Sammon, Quadratic convergence for cell-centered grids. Appl. Numer. Math.4 (1988) 377-394.
- 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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