On mixed error estimates for elliptic obstacle problems

Wenbin Liu*, Heping Ma, Tao TANG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We establish in this paper sharp error estimates of residual type for finite element approximation to elliptic obstacle problems. The estimates are of mixed nature, which are neither of a pure a priori form nor of a pure a posteriori form but instead they are combined by an a priori part and an a posteriori part. The key ingredient in our derivation for the mixed error estimates is the use of a new interpolator which enables us to eliminate inactive data from the error estimators. One application of our mixed error estimates is to construct a posteriori error indicators reliable and efficient up to higher order terms, and these indicators are useful in mesh-refinements and adaptive grid generations. In particular, by approximating the a priori part with some a posteriori quantities we can successfully track the free boundary for elliptic obstacle problems.

Original languageEnglish
Pages (from-to)261-283
Number of pages23
JournalAdvances in Computational Mathematics
Volume15
Issue number1-4
DOIs
Publication statusPublished - 2001

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Elliptic obstacle
  • Finite element approximation
  • Sharp a posteriori error estimates

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