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Finite element approximations of a glaciology problem

Published online by Cambridge University Press:  15 October 2004

Sum S. Chow ,
Graham F. Carey  and
Michael L. Anderson
Sum S. Chow
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA. [email protected].
Graham F. Carey
Affiliation:
ICES, Univ. of Texas at Austin, Austin, TX 78712, USA. [email protected].; [email protected].
Michael L. Anderson
Affiliation:
ICES, Univ. of Texas at Austin, Austin, TX 78712, USA. [email protected].; [email protected].
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Abstract

In this paper we study a model problem describing the movement of a glacier under Glen's flow law and investigated by Colinge and Rappaz [Colinge and Rappaz, ESAIM: M2AN33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in [Colinge and Rappaz, ESAIM: M2AN33 (1999) 395–406]. Supporting numerical convergence studies are carried out and we also demonstrate the numerical performance of an a posteriori error estimator in adaptive mesh refinement computation of the problem.

Keywords

Glen's flow lawnon-Newtonian fluidsfinite element error estimatessuccessive approximations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 5 , September 2004 , pp. 741 - 756
Copyright
© EDP Sciences, SMAI, 2004

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References

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