Journal of Scientific Computing

, Volume 15, Issue 3, pp 361–393

A Posteriori Error Estimators for a Class of Variational Inequalities

  • Wenbin Liu
  • Ningning Yan

DOI: 10.1023/A:1011130501691

Cite this article as:
Liu, W. & Yan, N. Journal of Scientific Computing (2000) 15: 361. doi:10.1023/A:1011130501691


In this paper, we present an a posteriori error analysis for the finite element approximation of a variational inequality. We derive a posteriori error estimators of residual type, which are shown to provide upper bounds on the discretization error for a class of variational inequalities provided the solutions are sufficiently regular. Furthermore we derive sharp a posteriori error estimators with both lower and upper error bounds for a subclass of the obstacle problem which are frequently met in many physical models. For sufficiently regular solutions, these estimates are shown to be equivalent to the discretization error in an energy type norm. Our numerical tests show that these sharp error estimators are both reliable and efficient in guiding mesh adaptivity for computing the free boundaries.

finite element approximationvariational inequalitiesa posteriori error estimatorsobstacle problems

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Wenbin Liu
    • 1
  • Ningning Yan
    • 2
  1. 1.CBS & Institute of Mathematics and StatisticsUniversity of KentCanterburyEngland
  2. 2.Academia SinicaInstitute of Systems ScienceBeijingPeople's Republic of China