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.
Classification : 65N12, 65N30
Mots clés : finite volumes, convection-diffusion equations, noncoercivity, non-regular data
@article{M2AN_2002__36_4_705_0, 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, pages = {705--724}, publisher = {EDP-Sciences}, volume = {36}, number = {4}, year = {2002}, doi = {10.1051/m2an:2002031}, zbl = {1070.65566}, mrnumber = {1932310}, language = {en}, url = {archive.numdam.org/item/M2AN_2002__36_4_705_0/} }
Droniou, Jérôme; 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, Tome 36 (2002) no. 4, pp. 705-724. doi : 10.1051/m2an:2002031. http://archive.numdam.org/item/M2AN_2002__36_4_705_0/
[1] Sobolev Spaces. Academic Press, New York (1975). | MR 450957 | Zbl 0314.46030
,[2] Convergence rate of a finite volume scheme for a two dimensional convection diffusion problem. ESAIM: M2AN 33 (1999) 493-516. | Numdam | Zbl 0937.65116
, and ,[3] Non-coercive linear elliptic problems. Potential Anal. 17 (2002) 181-203. | Zbl pre01785631
,[4] Ph.D. thesis, CMI, Université de Provence.
,[5] 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 0981.65095
, and ,[6] Convergence of finite volume approximations to the solutions of semilinear convection diffusion reaction equations. Numer. Math. 82 (1999) 91-116. | Zbl 0930.65118
, and ,[7] 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.
and ,[8] Quadratic convergence for cell-centered grids. Appl. Numer. Math. 4 (1988) 377-394. | Zbl 0651.65086
and ,[9] 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 1766855
, and ,