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

top
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

top

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

top
  1. [1] H. Blatter, Velocity and stress fields in grounded glaciers: A simple algorithm for including deviatoric stress gradients. J. Glaciology 41 (1995) 333–344. 
  2. [2] G.F. Carey, Computational Grids: Generation, Adaptation and Solution Strategies. Taylor & Francis (1997). Zbl0955.74001MR1483891
  3. [3] S.-S. Chow, Finite element error estimates for nonlinear elliptic equations of monotone type. Numer. Math. 54 (1989) 373–393. Zbl0643.65058
  4. [4] S.-S. Chow, Finite element error estimates for a blast furnace gas flow problem. SIAM J. Numer. Analysis 29 (1992) 769–780. Zbl0749.76040
  5. [5] S.-S. Chow and G.F. Carey, Numerical approximation of generalized Newtonian fluids using Heindl elements: I. Theoretical estimates. Internat. J. Numer. Methods Fluids 41 (2003) 1085–1118. Zbl1047.76040
  6. [6] J. Colinge and H. Blatter, Stress and velocity fields in glaciers: Part I. Finite-difference schemes for higher-order glacier models. J. Glaciology 44 (1998) 448–456. 
  7. [7] J. Colinge and J. Rappaz, A strongly nonlinear problem arising in glaciology. ESAIM: M2AN 33 (1999) 395–406. Zbl0946.65115
  8. [8] J.W. Glen, The Flow Law of Ice, Internat. Assoc. Sci. Hydrology Pub. 47, Symposium at Chamonix 1958 – Physics of the Movement of the Ice (1958) 171–183. 
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.