Skip to main content
SpringerLink
Log in

A Posteriori Estimators for the Finite Volume Discretization of an Elliptic Problem

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

We analyze a residual error estimator for a finite volume discretization of a linear elliptic boundary value problem. The error estimator consists of the residual of the strong equation and the jumps across the inter-element boundaries of a primal triangulation. Some numerical experiments are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Afif and B. Amaziane, Analysis of finite volume schemes for two-phase flow in porous media on unstructed grids, in: Finite Volume for Complex Applications, Vol. II, Problems and Perspectives, eds. F. Benkhaldoun and R. Vilsmeier (Hermés, Paris, 1999) pp. 387–394.

    Google Scholar 

  2. A. Agouzal, J.F. Maitre and F. Oudin, Un nouveau résultat d'estimation d'erreur pour les éléments finis mixtes rectangulaires avec intégration numérique. Aplication à l'analyse de schémas de type volumes finis, C. R. Acad. Sci. Paris Sér. I 322 (1996) 1225–1229.

    Google Scholar 

  3. I. Babuška and W.C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978) 736–754.

    Google Scholar 

  4. A. Bergam and Z. Mghazli, Estimateurs a posteriori d'un schéma de volumes finis pour un probléme non linéaire, C. R. Acad. Sci. Paris Sér. I 331 (2000) 475–478.

    Google Scholar 

  5. A. Bergam, Z. Mghazli and R. Verfürth, Estimations a posteriori d'un schéma de volumes finis pour un probléme non linéaire, Numer. Math. (electronic version) DOI 10.1007/s00211-003-0460-2 (2003).

  6. J. Bey, Finite-Volumen-und Mehrgitter-Verfahren für elliptische Randwertprobleme, in: Advances in Numerical Mathematics, Stuttgart (Teubner, Leipzig, 1998).

    Google Scholar 

  7. P.G. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland, Amesterdam, 1978).

    Google Scholar 

  8. P. Clément, Approximation by finite element functions using local regularization, RAIRO Anal. Numér. 9 (1975) 77–84.

    Google Scholar 

  9. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods, in: Handbook of Numerical Analysis, Vol. VII, eds. P.G. Ciarlet and J.-L. Lions (North-Holland, Amsterdam, 2000) pp. 713–1020.

    Google Scholar 

  10. S.V. Patankar, Numerical Heat Transfer and Fluid Flow, eds. Minkowyez and Sparrow, Series in Computational Methods in Mechanics and Thermal Sciences (McGraw-Hill, New York, 1980).

    Google Scholar 

  11. T. Sonar and E. Sülli, A dual graph-norm refinement indicator for finite volume approximations of the Euler equations, Numer. Math. 78 (1998) 619–658.

    Google Scholar 

  12. R. Verfürth, A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley and Teubner Mathematics (Wiley/Teubner, 1996).

  13. G. Voronoi, Nouvelles application des paramétres continus à la théorie des formes quadratures, J. Reine Angew. Math. 134 (1980) 198–287.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Cadi Ayyad, Faculté des Sciences Semlalia, B.P. 2390 Marrakech, Maroc

    M. Afif

  2. Dept. maths et info., Université Ibn Tofail, Faculté des Sciences, Laboratoire S.I.A.N.O., B.P. 133, Kénitra, Maroc

    A. Bergam & Z. Mghazli

  3. Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780, Bochum, Germany

    R. Verfürth

Authors
  1. M. Afif
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Bergam
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Z. Mghazli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. Verfürth
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Afif, M., Bergam, A., Mghazli, Z. et al. A Posteriori Estimators for the Finite Volume Discretization of an Elliptic Problem. Numerical Algorithms 34, 127–136 (2003). https://doi.org/10.1023/B:NUMA.0000005400.45852.f3

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:NUMA.0000005400.45852.f3

Search

Navigation