| Issue |
ESAIM: M2AN
Volume 38, Number 5, September-October 2004
|
|
|---|---|---|
| Page(s) | 741 - 756 | |
| DOI | https://doi.org/10.1051/m2an:2004033 | |
| Published online | 15 October 2004 | |
Finite element approximations of a glaciology problem
1
Department of Mathematics, Brigham Young University, Provo, UT
84602, USA. schow@math.byu.edu.
2
ICES, Univ. of Texas at Austin, Austin,
TX 78712, USA. carey@cfdlab.ae.utexas.edu.; michaela@rsp.com.au.
Received:
22
April
2003
Revised:
18
June
2004
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.
Mathematics Subject Classification: 26B25 / 35J20 / 35J60 / 49J45 / 65N30 / 86A40
Key words: Glen's flow law / non-Newtonian fluids / finite element error estimates / successive approximations.
© EDP Sciences, SMAI, 2004
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