Discrete sobolev inequalities and lp error estimates for finite volume solutions of convection diffusion equations

Mathematical Modelling and Numerical Analysis

Volumn 35, Issue 4, 2001, Pages 767-778

  Coudière, Yves ^a   Gallouët, Thierry ^b   Herbin, Raphaèle ^b  

^a INRIA   (France)

^b NONE

Author keywords

Convection diffusion equations; Finite volume methods; Lp error estimates; Unstructured meshes

Indexed keywords

EID: 0035537716     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2001135     Document Type: Article

References (27)

1. R.E. Bank and D.J. Rose, Some error estimates for the box method. SIAM J. Numer. Anal. 24 (1987) 777-787.
2. R. Belmouhoub, Modélisation tridimensionnelle de la genèse des bassins sédimentaires. Thesis, École Nationale Supérieure des Mines de Paris, France (1996).
3. Z. Cai, On the finite volume element method. Numer. Math. 58 (1991) 713-735.
4. Z. Cai, Mandel J. and S. Mc Cormick, The finite volume element method for diffusion equations on general triangulations. SIAM J. Numer. Anal. 28 (1991) 392-402.
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 J. 0566 (1995).
6. M. Dauge, Elliptic boundary value problems in corner domains. Lecture Notes in Math. 1341 Springer-Verlag, Berlin (1988).
7. Y. Coudière and P. Villedieu, A finite volume scheme for the linear convection-diffusion equation on locally refined meshes, in 7-th international colloquium on numerical analysis, Plovdiv, Bulgaria (1998).
8. Y. Coudière, J.P. Vila and P. Villedieu, Convergence of a finite volume scheme for a diffusion problem, in Finite volumes for complex applications, problems and perspectives, F. Benkhaldoun and R. Vilsmeier Eds., Hermès, Paris (1996) 161-168.
9. 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.
10. Y. Coudière and P. Villedieu, Convergence of a finite volume scheme for a two dimensional diffusion convection equation on locally refined meshes. ESAIM: M2AN 34 (2000) 1109-1295.
11. R. Eymard, T. Gallouët and R. Herbin, Convergence of finite volume schemes for semilinear convection diffusion equations. Numerische Mathematik. 82 (1999) 91-116.
12. R. Eymard and T. Gallouët, Convergence d'un schéma de type éléments finis-volumes finis pour un système couplé elliptique-hyperbolique. RAIRO Modél. Math. Anal. Numér. 27 (1993) 843-861.
13. R. Eymard, T. Gallouët and R. Herbin, The finite volume method, in Handbook of numerical analysis, P.G. Ciarlet and J.L. Lions, Eds., Elsevier Science BV, Amsterdam (2000) 715-1022.
14. 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.
15. P.A. Forsyth, A control volume finite element approach to NAPL groundwater contamination. SIAM J. Sci. Stat. Comput. 12 (1991) 1029-1057.
16. P.A. Forsyth and P.H. Sammon, Quadratic convergence for cell-centered grids. Appl. Numer. Math. 4 (1988) 377-394.
17. 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. 37 (2000) 1035-1072.
18. B. Heinrich, Finite difference methods on irregular networks. A generalized approach to second order elliptic problems. Internat. Ser. Numer. Math. 82, Birkhäuser-Verlag, Stuttgart (1987).
19. R. Herbin, An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh. Numer. Methods. Partial Differ. Equations 11 (1995) 165-173.
20. R. Herbin, Finite volume methods for diffusion convection equations on general meshes, in Finite volumes for complex applications, problems and perspectives, F. Benkhaldoun and R. Vilsmeier, Eds., Hermès, Paris (1996) 153-160.
21. F. Jacon and D. Knight, A Navier-Stokes algorithm for turbulent flows using an unstructured grid and flux difference splitting. AIAA J. 2292 (1994).
22. R.D. Lazarov and I.D. Mishev, Finite volume methods for reaction diffusion problems, in Finite volumes for complex applications, problems and perspectives, F. Benkhaldoun and R. Vilsmeier, Eds., Hermès, Paris (1996) 233-240.
23. R.D. Lazarov, I.D. Mishev and P.S. Vassilevski, Finite volume methods for convection-diffusion problems. SIAM J. Numer. Anal. 33 (1996) 31-55.
24. T.A. Manteufel and A.B. White, The numerical solution of second order boundary value problem on non uniform meshes. Math. Comput. 47 (1986) 511-536.
25. K.W. Morton and E. Süli, Finite volume methods and their analysis. IMA J. Numer. Anal. 11 (1991) 241-260.
26. D. Trujillo, Couplage espace-temps de schémas numériques en simulation de réservoir. Ph.D. Thesis, University of Pau, France (1994).
27. P.S. Vassileski, S.I. Petrova and R.D. Lazarov, Finite difference schemes on triangular cell-centered grids with local refinement. SIAM J. Sci. Statist. Comput. 13 (1992) 1287-1313.