no. 4
Finite volume methods for convection-diffusion equations with right-hand side in H -1
ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 4, pp. 705-724

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.

DOI : 10.1051/m2an:2002031
Classification : 65N12, 65N30
Keywords: finite volumes, convection-diffusion equations, noncoercivity, non-regular data 
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     author = {Droniou, J\'er\^ome and Gallou\"et, Thierry},
     title = {Finite volume methods for convection-diffusion equations with right-hand side in $H^{-1}$},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {705--724},
     year = {2002},
     publisher = {EDP Sciences},
     volume = {36},
     number = {4},
     doi = {10.1051/m2an:2002031},
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Droniou, Jérôme; Gallouët, Thierry. Finite volume methods for convection-diffusion equations with right-hand side in $H^{-1}$. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 4, pp. 705-724. doi: 10.1051/m2an:2002031

[1] R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). | Zbl | MR

[2] Y. Coudière, J.P. Vila and P. Villedieu, Convergence rate of a finite volume scheme for a two dimensional convection diffusion problem. ESAIM: M2AN 33 (1999) 493-516. | Zbl | Numdam

[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. | Zbl

[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. | Zbl

[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. | Zbl

[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). | MR

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