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Finite element approximations of a glaciology problem

Published online by Cambridge University Press:  15 October 2004

Sum S. Chow ,
Graham F. Carey  and
Michael L. Anderson
Sum S. Chow
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA. [email protected].
Graham F. Carey
Affiliation:
ICES, Univ. of Texas at Austin, Austin, TX 78712, USA. [email protected].; [email protected].
Michael L. Anderson
Affiliation:
ICES, Univ. of Texas at Austin, Austin, TX 78712, USA. [email protected].; [email protected].
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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: M2AN33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in [Colinge and Rappaz, ESAIM: M2AN33 (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.

Keywords

Glen's flow lawnon-Newtonian fluidsfinite element error estimatessuccessive approximations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 5 , September 2004 , pp. 741 - 756
Copyright
© EDP Sciences, SMAI, 2004

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References

Blatter, H., Velocity and stress fields in grounded glaciers: A simple algorithm for including deviatoric stress gradients. J. Glaciology 41 (1995) 333–344. CrossRef
G.F. Carey, Computational Grids: Generation, Adaptation and Solution Strategies. Taylor & Francis (1997).
Chow, S.-S., Finite element error estimates for nonlinear elliptic equations of monotone type. Numer. Math. 54 (1989) 373–393. CrossRef
Chow, S.-S., Finite element error estimates for a blast furnace gas flow problem. SIAM J. Numer. Analysis 29 (1992) 769–780. CrossRef
Chow, S.-S. and Carey, G.F., Numerical approximation of generalized Newtonian fluids using Heindl elements: I. Theoretical estimates. Internat. J. Numer. Methods Fluids 41 (2003) 1085–1118. CrossRef
Colinge, J. and Blatter, H., Stress and velocity fields in glaciers: Part I. Finite-difference schemes for higher-order glacier models. J. Glaciology 44 (1998) 448–456. CrossRef
Colinge, J. and Rappaz, J., A strongly nonlinear problem arising in glaciology. ESAIM: M2AN 33 (1999) 395–406. CrossRef
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.
Glowinski, R. and Rappaz, J., Approximation of a nonlinear elliptic problem arising in a non-Newtonian fluid flow model in glaciology. ESAIM: M2AN 37 (2003) 175–186. CrossRef
Han, W., Soren, J. and Shimansky, I., The Kačanov method for some nonlinear problems. Appl. Num. Anal. 24 (1997) 57–79.
Johnson, C. and Thomee, V., Error estimates for a finite element approximation of a minimal surface. Math. Comp. 29 (1975) 343–349. CrossRef
Liu, W.B. and Barrett, J.W., Finite element approximation of some degenerate monotone quasilinear elliptic systems. SIAM J. Numer. Analysis 33 (1996) 98–106.
W.S.B. Patterson, The Physics of Glaciers, 2nd edition. Pergamon Press (1981).
E. Zeidler, Nonlinear Functional Analysis and Its Applications II/B. Nonlinear Monotone Operators, Springer-Verlag (1990).