Finite element approximations of a glaciology problem

Sum S. Chow; Graham F. Carey; Michael L. Anderson

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2004)

  • Volume: 38, Issue: 5, page 741-756
  • ISSN: 0764-583X

Abstract

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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: 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.

How to cite

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Chow, Sum S., Carey, Graham F., and Anderson, Michael L.. "Finite element approximations of a glaciology problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.5 (2004): 741-756. <http://eudml.org/doc/245931>.

@article{Chow2004,
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: 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.},
author = {Chow, Sum S., Carey, Graham F., Anderson, Michael L.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Glen’s flow law; non-newtonian fluids; finite element error estimates; successive approximations},
language = {eng},
number = {5},
pages = {741-756},
publisher = {EDP-Sciences},
title = {Finite element approximations of a glaciology problem},
url = {http://eudml.org/doc/245931},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Chow, Sum S.
AU - Carey, Graham F.
AU - Anderson, Michael L.
TI - Finite element approximations of a glaciology problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 5
SP - 741
EP - 756
AB - 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.
LA - eng
KW - Glen’s flow law; non-newtonian fluids; finite element error estimates; successive approximations
UR - http://eudml.org/doc/245931
ER -

References

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  2. [2] G.F. Carey, Computational Grids: Generation, Adaptation and Solution Strategies. Taylor & Francis (1997). Zbl0955.74001MR1483891
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  9. [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. Zbl1046.76002
  10. [10] W. Han, J. Soren and I. Shimansky, The Kačanov method for some nonlinear problems. Appl. Num. Anal. 24 (1997) 57–79. Zbl0878.65099
  11. [11] C. Johnson and V. Thomee, Error estimates for a finite element approximation of a minimal surface. Math. Comp. 29 (1975) 343–349. Zbl0302.65086
  12. [12] W.B. Liu and J.W. Barrett, Finite element approximation of some degenerate monotone quasilinear elliptic systems. SIAM J. Numer. Analysis 33 (1996) 98–106. Zbl0846.65064
  13. [13] W.S.B. Patterson, The Physics of Glaciers, 2nd edition. Pergamon Press (1981). 
  14. [14] E. Zeidler, Nonlinear Functional Analysis and Its Applications II/B. Nonlinear Monotone Operators, Springer-Verlag (1990). Zbl0684.47029MR1033498

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