Numerische Mathematik

, Volume 59, Issue 1, pp 107–127

On the asymptotic exactness of error estimators for linear triangular finite elements

  • Ricardo Durán
  • María Amelia Muschietti
  • Rodolfo Rodríguez
Article

DOI: 10.1007/BF01385773

Cite this article as:
Durán, R., Muschietti, M.A. & Rodríguez, R. Numer. Math. (1991) 59: 107. doi:10.1007/BF01385773

Summary

This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of elliptic problems. We analyze two estimators based on recovery operators for the gradient of the approximate solution. By using superconvergence results we prove their asymptotic exactness under regularity assumptions on the mesh and the solution.

One of the estimators can be easily computed in terms of the jumps of the gradient of the finite element approximation. This estimator is equivalent to the error in the energy norm under rather general conditions. However, we show that for the asymptotic exactness, the regularity assumption on the mesh is not merely technical. While doing this, we analyze the relation between superconvergence and asymptotic exactness for some particular examples.

Subject classifications

AMS(MOS) 65N30 65N15 CR: G1.8 

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Ricardo Durán
    • 1
  • María Amelia Muschietti
    • 1
  • Rodolfo Rodríguez
    • 1
  1. 1.Departamento de Matemática, Facultad de Ciencias ExactasUNLPLa PlataArgentina
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA
  3. 3.Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

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