Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 3, pp. 493-516. 
@article{M2AN_1999__33_3_493_0,
     author = {Coudi\`ere, Yves and Vila, Jean-Paul and Villedieu, Philippe},
     title = {Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {493--516},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {3},
     year = {1999},
     mrnumber = {1713235},
     zbl = {0937.65116},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1999__33_3_493_0/}
}
TY  - JOUR
AU  - Coudière, Yves
AU  - Vila, Jean-Paul
AU  - Villedieu, Philippe
TI  - Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1999
SP  - 493
EP  - 516
VL  - 33
IS  - 3
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/M2AN_1999__33_3_493_0/
LA  - en
ID  - M2AN_1999__33_3_493_0
ER  - 
%0 Journal Article
%A Coudière, Yves
%A Vila, Jean-Paul
%A Villedieu, Philippe
%T Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1999
%P 493-516
%V 33
%N 3
%I EDP-Sciences
%U http://archive.numdam.org/item/M2AN_1999__33_3_493_0/
%G en
%F M2AN_1999__33_3_493_0
Coudière, Yves; Vila, Jean-Paul; Villedieu, Philippe. Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 3, pp. 493-516. http://archive.numdam.org/item/M2AN_1999__33_3_493_0/

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

[2] M. Aftosmis, D. Gaitonde and T. Sean Tavares, On the accuracy, stability and monotonicity of various reconstruction algorithms for unstructured meshes. AIAA paper No. 94-0415 (1994).

[3] J. Baranger, J. F. Maitre and F. Oudin, Connection between finite volume and mixed finite element methods. RAIRO Modél. Math. Anal. Num. 30 (1996) 445-465. | Numdam | MR | Zbl

[4] W. J. Coirier, An Adaptatively-Refined, Cartesian, Cell-based Scheme for the Euler and Navier-Stokes Equations. Ph. D. thesis, Michigan University, NASA Lewis Research Center, USA (1994).

[5] W. J. Coirier and K. G. Powell, A Cartesian, cell-based approach for adaptative-refined solutions of the Euler and Navier-Stokes equations. AIAA (1995).

[6] Y. Coudière, Analyse de schémas volumes finis sur maillages non structurés pour des problèmes linéaires hyperboliques et elliptiques. Ph. D. thesis, Paul Sabatier University, France (1998).

[7] M. Dauge, Elliptic Boundary Value Problems in Corner Domains. Lect. Notes Math. 1341, Springer Verlag, Berlin-New York (1988). | MR | Zbl

[8] F. Dubois, Interpolation de Lagrange et volumes finis. Une technique nouvelle pour calculer le gradient d'une fonction sur les faces d'un maillage non structuré. Technical report, Aérospatiale (1992).

[9] I. Faille, A control volume method to solve an elliptic equation on a 2d irregular meshing. Comput. Methods. Appl. Mech. Engrg. 100 (1992) 275-290. | MR | Zbl

[10] T. Gallouët, An introduction to finite volume methods. Technical report, Cours CEA/EDF/INRIA (1992).

[11] W. Guo and M. Stynes, An analysis of a cell-vertex finite volume method for a parabohe convection-diffusion problem. Math. Comp. 66 (1997) 105-124. | MR | Zbl

[12] R. Herbin, An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh. Numerical Method for Partial Differential Equations 11 (1994) 165-173. | MR | Zbl

[13] R. Herbin, Finite volume methods for diffusion convection equations on general meshes, in Finite Volumes for Complex Applications, Hermès (1996) 153-160.

[14] F. Jacon and D. Knight, A Navier-Stokes algorithm for turbulent flows using an unstructured grid and flux difference splitting. AIAA paper No. 94-2292 (1994).

[15] C.R. Mitchell and R.W. Walters, K-exect reconstruction for the Navier-Stokes equations on arbitrary grids. AIAA (1993).

[16] K.W. Morton and E. Süli, Finite volume methods and their analysis. IMA J. Numer. Anal. 11 (1991) 241-260. | MR | Zbl

[17] E. Süli, Convergence of finite volume schemes for Poisson's equation on nonuniform meshes. SIAM J. Numer. Anal. 28 (1991) 1419-1430. | MR | Zbl

[18] J.-M. Thomas and D. Trujillo, Analysis of finite volumes methods. Technical Report 95/19, CNRS, URA 1204 (1995).

[19] J.-M. Thomas and D. Trujillo, Convergence of finite volumes methods. Technical Report 95/20, CNRS, URA 1204 (1995).

[20] D. Trujillo, Couplage espace-temps de schémas numériques en simulation de réservoir. Ph.D. thesis, University of Pau et pays de l'Adour (1994).

[21] S. Verdière and M.H. Vignal, Numerical and theoretical study of a dual mesh method using finite volume schemes for two phase flow problems in porous media. Numer. Math. 80 (1998) 601-639. | MR | Zbl

[22] P. Villedieu, Une méthode de volumes finis sur maillages non-structurés quelconques pour l'équation de convection diffusion. Technical Report 1-3550.00-DERI, ONERA (1996).