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 language | English |
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Pages (from-to) | 261-283 |
Number of pages | 23 |
Journal | Advances in Computational Mathematics |
Volume | 15 |
Issue number | 1-4 |
DOIs | |
Publication status | Published - 2001 |
Scopus Subject Areas
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- Elliptic obstacle
- Finite element approximation
- Sharp a posteriori error estimates