Finite element approximations of a glaciology problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 5, p. 741-756

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: M2AN 33 (1999) 395-406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis 29 (1992) 769-780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis 33 (1996) 98-106] and give an analysis of the convergence of the successive approximations used in [Colinge and Rappaz, ESAIM: M2AN 33 (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.

DOI : https://doi.org/10.1051/m2an:2004033
Classification:  26B25,  35J20,  35J60,  49J45,  65N30,  86A40
Keywords: Glen's flow law, non-newtonian fluids, finite element error estimates, successive approximations
@article{M2AN_2004__38_5_741_0,
     author = {Chow, Sum S. and Carey, Graham F. and Anderson, Michael L.},
     title = {Finite element approximations of a glaciology problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {5},
     year = {2004},
     pages = {741-756},
     doi = {10.1051/m2an:2004033},
     zbl = {1130.86300},
     mrnumber = {2104426},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2004__38_5_741_0}
}
Chow, Sum S.; Carey, Graham F.; Anderson, Michael L. Finite element approximations of a glaciology problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 5, pp. 741-756. doi : 10.1051/m2an:2004033. http://www.numdam.org/item/M2AN_2004__38_5_741_0/

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