Numerische Mathematik

, Volume 62, Issue 1, pp 297–303 | Cite as

On the asymptotic exactness of Bank-Weiser's estimator

  • Ricardo Durán
  • Rodolfo Rodríguez


In this paper we analyze an error estimator introduced by Bank and Weiser. We prove that this estimator is asymptotically exact in the energy norm for regular solutions and parallel meshes. By considering a simple example we show that this is not true for general meshes.

Mathematics Subject Classification (1991)

65N30 65N50 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Babuška, I., Durán, R., Rodríguez, R. (1992): Analysis of the efficiency of an a-posteriori error estimator for linear triangular finite elements. SIAM J. Numer. Anal. (to appear)Google Scholar
  2. 2.
    Babuška, I., Miller, A. (1987): A feedback finite element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimator. Comput. Methods Appl. Mech. Eng.61, 1–40Google Scholar
  3. 3.
    Babuška, I., Rheinboldt, W.C. (1978): Error estimates for adaptive finite element computations. SIAM J. Numer. Anal.15, 736–754CrossRefGoogle Scholar
  4. 4.
    Babuška, I., Rodríguez, R. (1991): The problem of the selection of an a-posteriori error indicator based on smoothening techniques. Tech. Note BN-1126, IPST, University of MarylandGoogle Scholar
  5. 5.
    Bank, R.E. (1990): PLTMG. A software package for solving, elliptic partial differential equations. Users guide 6.0. SIAM, PhiladelphiaGoogle Scholar
  6. 6.
    Bank, R.E., Weiser, A. (1985): Some a posteriori error estimators for elliptic partial differential equations. Math. Comput.44, 283–301Google Scholar
  7. 7.
    Bank, R.E., Welfert, B.D. (1991): A posteriori error estimates for the Stokes problem. SIAM J. Numer. Anal.28, 591–623Google Scholar
  8. 8.
    Bank, R.E., Welfert, B.D. (1990): A posteriori error estimates for the Stokes equations: a comparison. Comput. Methods Appl. Mech. Eng.82, 323–340Google Scholar
  9. 9.
    Durán, R., Muschietti, M.A., Rodríguez, R. (1991): On the asymptotic exactness of error estimators for linear triangular finite elements. Numer. Math.59, 107–127Google Scholar
  10. 10.
    Grisvard, P. (1985): Elliptic Problems in Nonsmooth Domains. Pitman, BostonGoogle Scholar
  11. 11.
    Krîzěk, M., Neittaanmäki, P. (1987): On superconvergence techniques. Acta Aplicandae Mathematicae9, 175–198Google Scholar
  12. 12.
    Lin, Q. (1992): Interpolated finite elements and global error expansions. (to appear)Google Scholar
  13. 13.
    Verfürth, R. (1989): A posteriori error estimators for the Stokes equations. Numer. Math.55, 309–325Google Scholar
  14. 14.
    Wheeler, M.F., Whiteman, J.R. (1987): Superconvergent recovery of gradients on subdomains from piecewise linear finite-element approximations. Numer. Methods for PDEs3, 357–374Google Scholar
  15. 15.
    Zienkiewicz, O.C., Zhu, J.Z. (1987): A simple error estimator and adaptive procedure for practical engineering analysis. Internat. J. Numer. Meth. Eng.24, 337–357Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Ricardo Durán
    • 1
  • Rodolfo Rodríguez
    • 1
  1. 1.Departamento de Matemática, Facultad de Ciencias ExactasUniversidad Nacional de la PlataLa PlataArgentina

Personalised recommendations