Summary
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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)
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, 1–40
Babuška, I., Rheinboldt, W.C. (1978): Error estimates for adaptive finite element computations. SIAM J. Numer. Anal.15, 736–754
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 Maryland
Bank, R.E. (1990): PLTMG. A software package for solving, elliptic partial differential equations. Users guide 6.0. SIAM, Philadelphia
Bank, R.E., Weiser, A. (1985): Some a posteriori error estimators for elliptic partial differential equations. Math. Comput.44, 283–301
Bank, R.E., Welfert, B.D. (1991): A posteriori error estimates for the Stokes problem. SIAM J. Numer. Anal.28, 591–623
Bank, R.E., Welfert, B.D. (1990): A posteriori error estimates for the Stokes equations: a comparison. Comput. Methods Appl. Mech. Eng.82, 323–340
Durán, R., Muschietti, M.A., Rodríguez, R. (1991): On the asymptotic exactness of error estimators for linear triangular finite elements. Numer. Math.59, 107–127
Grisvard, P. (1985): Elliptic Problems in Nonsmooth Domains. Pitman, Boston
Krîzěk, M., Neittaanmäki, P. (1987): On superconvergence techniques. Acta Aplicandae Mathematicae9, 175–198
Lin, Q. (1992): Interpolated finite elements and global error expansions. (to appear)
Verfürth, R. (1989): A posteriori error estimators for the Stokes equations. Numer. Math.55, 309–325
Wheeler, M.F., Whiteman, J.R. (1987): Superconvergent recovery of gradients on subdomains from piecewise linear finite-element approximations. Numer. Methods for PDEs3, 357–374
Zienkiewicz, O.C., Zhu, J.Z. (1987): A simple error estimator and adaptive procedure for practical engineering analysis. Internat. J. Numer. Meth. Eng.24, 337–357
Author information
Authors and Affiliations
Additional information
The work was partially supported by Fundación Antorchas.
The work was partially supported by the NSF under grant CCR-88-20279.