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glen's flow law

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Finite element approximations of a glaciology problem
Sum S. Chow, Graham F. Carey, Michael L. Anderson
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 38 / Issue 5 / September 2004

Published online by Cambridge University Press:

15 October 2004, pp. 741-756

Print publication:

September 2004
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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.