Some a Posteriori Error Estimators for p-Laplacian Based on Residual Estimation or Gradient Recovery

Liu, Steve Wenbin and Yan, Ningning (2001) Some a Posteriori Error Estimators for p-Laplacian Based on Residual Estimation or Gradient Recovery. Journal of Scientific Computing, 16 (4). pp. 435-477. ISSN 0885-7474. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1023/A:1013246424707

Abstract

n this paper, we first derive a posteriori error estimators of residual type for the finite element approximation of the p-Laplacian, and show that they are reliable, and efficient up to higher order terms. We then construct some a posteriori error estimators based on gradient recovery. We further compare the two types of a posteriori error estimators. It is found that there exist some relationships between the two types of estimators, which are similar to those held in the case of the Laplacian. It is shown that the a posteriori error estimators based on gradient recovery are equivalent to the discretization error in a quasi-norm provided the solution is sufficiently smooth and mesh is uniform. Under stronger conditions, superconvergnece properties have been established for the used gradient recovery operator, and then some of the gradient recovery based estimates are further shown to be asymptotically exact to the discretization error in a quasi-norm. Numerical results demonstrating these a posteriori estimates are also presented.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Social Sciences > Kent Business School
Depositing User: Steve Wenbin Liu
Date Deposited: 29 Jun 2011 12:45
Last Modified: 23 Jun 2014 11:07
Resource URI: http://kar.kent.ac.uk/id/eprint/22905 (The current URI for this page, for reference purposes)
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