Convergence of finite volume schemes for semilinear convection diffusion equations

Numerische Mathematik

Volumn 82, Issue 1, 1999, Pages 91-116

  Eymard, Robert ^a   Gallouët, Thierry ^b   Herbin, Raphaèle ^b  

^a UNIVERSITÉ PARIS EST   (France)

^b AIX MARSEILLE UNIVERSITY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039526846     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050412     Document Type: Article

References (26)

1. Agouzal, A., Baranger, J., Maitre, J.-F., Oudin F. (1995): Connection between finite volume and mixed finite element methods for a diffusion problem with non constant coefficients, with application to Convection Diffusion. East-West J. Num. Math. 3(4), 237-254
2. Bank, R.E., Rose, D.J. (1987): Some error estimates for the box method. SIAM J. Numer. Anal. 24(4), 777-787
3. Baranger, J., Maitre, J.-F., Oudin, F. (1996): Connection between finite volume and mixed finite element methods. Modél. Math. Anal. Numér., 30, 3, 4, 444-465
4. Cai, Z. (1991): On the finite volume element method, Num. Math. 58, 713-735
5. Cai, Z., Mandel, J., Mc Cormick, S. (1991): The finite volume element method for diffusion equations on general triangulations. SIAM J. Numer. Anal. 28(2), 392-402
6. Coudière, Y., Vila, J.P., Villedieu, P.: Convergence of a finite volume scheme for a diffusion problem, In: Benkhaldoun, F., Vilsmeier, R. (eds.), Finite volumes for complex applications, Problems and Perspectives (Hermes, Paris), 161-168
7. Deimling, K.: Nonlinear Functional Analysis, (Springer, New York)
8. Eymard, R., Gallouët, T. (1993): Convergence d'un schéma de type eléments finis - volumes finis pour un système couplé elliptique - hyperbolique, Modél. Math. Anal. Numér. 27(7), 843-861
9. Eymard, R., Gallouët, T., Herbin, R.: The finite volume method, to appear in Ciarlet, P.G., Lions, J.L. (eds.), Handbook of Numerical Analysis, North-Holland
10. Faille, I. (1992): A control volume method to solve an elliptic equation on a 2D irregular meshing. Comp. Meth. Appl. Mech. Engrg., 100, 275-290
11. Feistauer M., Felcman, J., Lukacova-Medvidova, M.: On the convergence of a combined finite volume-finite element method for nonlinear convection- diffusion problems, Numer. Meth. for P.D.E.'s, to appear.
12. Forsyth, P.A. (1989): A control volume finite element method for local mesh refinement. SPE 18415, 85-96
13. Forsyth, P.A. (1991): A control volume finite element approach to NAPL groundwater contamination. SIAM J. Sci. Stat. Comput. 12(5), 1029-1057
14. Forsyth, P.A., Sammon, P.H. (1988): Quadratic Convergence for Cell-Centered Grids. Appl. Num. Math. 4, 377-394
15. Herbin R. (1995): An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh. Num. Meth. P.D.E. 11, 165-173
16. Herbin R. (1996): Finite volume methods for diffusion convection equations on general meshes, in Finite volumes for complex applications, Problems and Perspectives, Benkhaldoun, F., Vilsmeier, R. (eds.), Hermes, 153-160
17. Herbin R., Labergerie, O. (1997): Finite volume schemes for elliptic and elliptic-hyperbolic problems on triangular meshes, Comp. Meth. Appl. Mech. Engin. 147, 85-103
18. Lazarov, R.D., Mishev, I.D. (1996): Finite volume methods for reaction diffusion problems. In: Benkhaldoun, F., Vilsmeier, R. (eds.), Finite volumes for complex applications, Problems and Perspectives. (Hermes, Paris), 233-240
19. Lazarov, R.D., Mishev, I.D., Vassilevski, P.S (1996): Finite volume methods for convection-diffusion problems. SIAM J. Numer. Anal. 33, 31-55
20. Manteufel, T.A., White, A.B. (1986): The numerical solution of second order boundary value problem on non uniform meshes, Math. Comput. 47, 511-536
21. Mishev, I.D.: Finite volume methods on Voronoi meshes, to appear
22. Morton, K.W., Süli, E. (1991): Finite volume methods and their analysis. IMA J. Numer. Anal. 11, 241-260
23. Patankar, S.V. (1980): Numerical Heat Transfer and Fluid Flow, Series in Computational Methods in Mechanics and Thermal Sciences, Minkowycz, Sparrow Eds. (Mc Graw Hill)
24. Vanselow, R. (1996): Relations between FEM and FVM. In: Benkhaldoun, F., Vilsmeier, R. (eds.), Finite volumes for complex applications, Problems and Perspectives (Hermes, Paris), 217-223
25. Vignal, M.H. (1996): Convergence of a finite volume scheme for a system of an elliptic equation and a hyperbolic equation Modél. Math. Anal. Numér. 30(7), 841-872
26. Vignal M.H. (1996): Convergence of Finite Volumes Schemes for an elliptic hyperbolic system with boundary conditions. In: Benkhaldoun, F., Vilsmeier, R. (eds.), Finite volumes for complex applications, Problems and Perspectives (Hermes, Paris), 145-152