Numerische Mathematik

, Volume 84, Issue 4, pp 527–548

Residual type a posteriori error estimates for elliptic obstacle problems

  • Zhiming Chen
  • Ricardo H. Nochetto
Original article

DOI: 10.1007/s002110050009

Cite this article as:
Chen, Z. & Nochetto, R. Numer. Math. (2000) 84: 527. doi:10.1007/s002110050009


A posteriori error estimators of residual type are derived for piecewise linear finite element approximations to elliptic obstacle problems. An instrumental ingredient is a new interpolation operator which requires minimal regularity, exhibits optimal approximation properties and preserves positivity. Both upper and lower bounds are proved and their optimality is explored with several examples. Sharp a priori bounds for the a posteriori estimators are given, and extensions of the results to double obstacle problems are briefly discussed.

Mathematics Subject Classification (1991): 65N15, 65N30; 41A05, 41A29, 41A36 

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Zhiming Chen
    • 1
  • Ricardo H. Nochetto
    • 2
  1. 1.Institute of Mathematics, Academia Sinica, Beijing 100080, PR China CN
  2. 2.Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA US

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