Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem

Mathematical Modelling and Numerical Analysis

Volumn 33, Issue 3, 1999, Pages 493-516

  Coudière, Yves ^a   Vila, Jean Paul ^a   Villedieu, Philippe ^b  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b ONERA   (France)

Author keywords

Convection diffusion; Convergence rate; Finite volumes; Unstructured meshes

Indexed keywords

EID: 0039938830     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:1999149     Document Type: Article

References (22)

1. R.A. Adams, Sobolev Spaces. Academic Press, New-York (1975).
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.
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 lináires 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).
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.
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 parabolic convection-diffusion problem. Math. Comp. 66 (1997) 105-124.
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.
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.
17. E. Süli, Convergence of finite volume schemes for Poisson's equation on nonuniform meshes. SIAM J. Numer. Anal. 28 (1991) 1419-1430.
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.
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).