Quasi Norm a Posteriori Error Estimates Based on Gradient Recovery or Residual Estimation

Liu, Wenbin and Yan, Ningning (2001) Quasi Norm a Posteriori Error Estimates Based on Gradient Recovery or Residual Estimation. Journal of Scientific Computing, 16 (4). pp. 435-477. ISSN 0885-7474. (doi:https://doi.org/10.1023/A:1013246424707) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Abstract

In 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
Uncontrolled keywords:	Finite element approximation; p-Laplacian; a posteriori error estimators; quasi-norm; gradient recovery; superconvergence.
Subjects:	H Social Sciences > HA Statistics > HA33 Management Science
Divisions:	Faculties > Social Sciences > Kent Business School
Depositing User:	Steve Wenbin Liu
Date Deposited:	14 Nov 2008 10:04 UTC
Last Modified:	07 Mar 2017 09:28 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/8521 (The current URI for this page, for reference purposes)