no. 5
Finite element approximations of a glaciology problem
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 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 : 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 
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     title = {Finite element approximations of a glaciology problem},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {741--756},
     year = {2004},
     publisher = {EDP Sciences},
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     doi = {10.1051/m2an:2004033},
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     zbl = {1130.86300},
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     url = {https://www.numdam.org/articles/10.1051/m2an:2004033/}
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Chow, Sum S.; Carey, Graham F.; Anderson, Michael L. Finite element approximations of a glaciology problem. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 741-756. doi: 10.1051/m2an:2004033

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[4] S.-S. Chow, Finite element error estimates for a blast furnace gas flow problem. SIAM J. Numer. Analysis 29 (1992) 769-780. | Zbl

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[7] J. Colinge and J. Rappaz, A strongly nonlinear problem arising in glaciology. ESAIM: M2AN 33 (1999) 395-406. | Zbl | Numdam

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[9] R. Glowinski and J. Rappaz, Approximation of a nonlinear elliptic problem arising in a non-Newtonian fluid flow model in glaciology. ESAIM: M2AN 37 (2003) 175-186. | Zbl | Numdam

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