Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes

Yves Coudière; Philippe Villedieu

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 6, page 1123-1149
  • ISSN: 0764-583X

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Coudière, Yves, and Villedieu, Philippe. "Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.6 (2000): 1123-1149. <http://eudml.org/doc/194030>.

@article{Coudière2000,
author = {Coudière, Yves, Villedieu, Philippe},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mesh refinement; convection-diffusion equation; finite volume method; convergence; error estimate},
language = {eng},
number = {6},
pages = {1123-1149},
publisher = {Dunod},
title = {Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes},
url = {http://eudml.org/doc/194030},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Coudière, Yves
AU - Villedieu, Philippe
TI - Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 6
SP - 1123
EP - 1149
LA - eng
KW - mesh refinement; convection-diffusion equation; finite volume method; convergence; error estimate
UR - http://eudml.org/doc/194030
ER -

References

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  1. [1] R.E. Bank and D.J. Rose, Some error estimates for the box method. SIAM J. Numer. Anal. 24 (1987) 777 787. Zbl0634.65105MR899703
  2. [2] J. Baranger, J.F. Maitre and F. Oudin, Connection between finite volume and mixed finite element methods. RAIRO Modél. Math. Anal. Numér. 30 (1996) 445-465. Zbl0857.65116MR1399499
  3. [3] M.J. Berger and P. Collela, Local adaptative mesh refinement for shock hydrodynamics. J. Comput. Phys. 82 (1989) 64-84. Zbl0665.76070
  4. [4] Z. Cai, On the finite volume element method. Numer. Math. 58 (1991) 713-735. Zbl0731.65093MR1090257
  5. [5] Z. Cai, J. Mandel and S. McCormick, The finite volume element method for diffusion equations on general triangulations. SIAM J. Numer. Anal. 28 (1991) 392-402. Zbl0729.65086MR1087511
  6. [6] Z. Cai and S. McCormick, On the accuracy of the finite volume element method for diffusion equations on composite grids. SIAM J. Numer. Anal 27 (1990) 636-655. Zbl0707.65073MR1041256
  7. [7] W.J. Coirier, An Adaptatively-Refined, Cartesian, Cell-based Scheme for the Euler and Navier-Stokes Equations. Ph.D. thesis, Michigan Univ., NASA Lewis Research Center (1994). 
  8. [8] 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). 
  9. [9] Y. Coudière, Analyse de schémas volumes finis sur maillages non structurés pour des problèmes linéaires hyperboliques et elliptiques. Ph.D. thesis, Université Paul Sabatier (1999). 
  10. [10] Y. Coudière, T. Gallouët and R. Herbin, Discrete sobolev inequalities and lp error estimates for approximate finite volume solutions of convection diffusion equation. Preprint of LATP, University of Marseille 1, 98-13 (1998). 
  11. [11] Y. Coudière, J.P. Vila and P. Villedieu, Convergence rate of a finite volume scheme for a two dimensionnal diffusion convection problem. ESAIM: M2AN 33 (1999) 493-516. Zbl0937.65116MR1713235
  12. [12] B. Courbet and J.P. Croisille, Finite volume box schemes on triangular meshes. RAIRO Modél. Math. Anal. Numér. 32 (1998) 631-649. Zbl0920.65065MR1643473
  13. [13] M. Dauge, Elliptic Boundary Value Problems in Corner Domains. Lect. Notes Math., Springer-Verlag, Berlin (1988). Zbl0668.35001MR961439
  14. [14] R.E. Ewing, R.D. Lazarov and P.S. Vassilevski, Local refinement techniques for elliptic problems on cell-centered grids. I. Error analysis. Math. Comp. 56 (1991) 437-461. Zbl0724.65093MR1066831
  15. [15] R. Eymard, T. Gallouët and R. Herbin, Finite volume methods, in Handbook of Numerical Analysis, P.G. Ciarlet and J.L. Lions Eds. (to appear). Prépublication No 97-19 du LATP, UMR 6632, Marseille (1997). Zbl0981.65095MR1804748
  16. [16] P.A. Forsyth and P.H. Sammon, Quadratic convergence for cell-centered grids. Appl Numer. Math. 4 (1988) 377-394. Zbl0651.65086MR948505
  17. [17] B. Heinrich, Finite Difference Methods on Irregular Networks. Internat. Ser. Numer. Anal. 82, Birkhaüser, Verlag Basel (1987). Zbl0623.65096MR875416
  18. [18] R. Herbin, An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh. Numer. Methods Partial Differential Equations 11 (1994) 165-173. Zbl0822.65085MR1316144
  19. [19] F. Jacon and D. Knight, A Navier-Stokes algorithm for turbulent flows using an unstructured grid and flux difference splitting. AIAA (1994). 
  20. [20] H. Jianguo and X. Shitong, On the finite volume element method for general self-adjoint elliptic problem. SIAM J. Numer. Anal. 35 (1998) 1762-1774. Zbl0913.65097MR1640017
  21. [21] P. Lesaint, Sur la résolution des systèmes hyperboliques du premier ordre par des méthodes d'éléments finis. Technical report, CEA (1976). 
  22. [22] T.A. Manteuffel and A.B. White, The numerical solution of second-order boundary values problems on nonuniform meshes. Math. Comp. 47 (1986) 511-535. Zbl0635.65092MR856700
  23. [23] K. Mer, Variational analysis of a mixed finite element finite volume scheme on general triangulations. Technical Report 2213, INRIA, Sophia Antipolis (1994). Zbl0961.76045
  24. [24] I.D. Mishev, Finite volume methods on voronoï meshes. Numer. Methods Partial Differential Equations 14 (1998) 193-212. Zbl0903.65083MR1605410
  25. [25] K.W. Morton and E. Süli, Finite volume methods and their analysis. IMA J. Numer. Anal. 11 (1991) 241-260. Zbl0729.65087MR1105229
  26. [26] E. Süli, Convergence of finite volume schemes for Poisson's equation on nonuniform meshes. SIAM J. Numer. Anal. 28 (1991) 1419-1430. Zbl0802.65104MR1119276
  27. [27] J.-M. Thomas and D. Trujillo. Analysis of finite volumes methods. Technical Report 95/19, CNRS, URA 1204 (1995). 
  28. [28] J.-M. Thomas and D. Trujillo, Convergence of finite volumes methods. Technical Report 95/20, CNRS, URA 1204 (1995). 
  29. [29] R. Vanselow and H.P. Scheffler, Convergence analysis of a finite volume method via a new nonconforming finite element method. Numer. Methods Partial Differential Equations 14 (1998) 213-231. Zbl0903.65084MR1605414
  30. [30] P.S. Vassilevski, S.I. Petrova and R.D. Lazarov. Finite difference schemes on triangular cell-centered grids with local refinement. SIAM J. Sci. Stat. Comput. 13 (1992) 1287-1313. Zbl0813.65115MR1185647
  31. [31] A. Weiser and M.F. Wheeler, On convergence of block-centered finite differences for elliptic problems. SIAM J. Numer. Anal. 25 (1988) 351-375. Zbl0644.65062MR933730

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