# Finite element approximations of a glaciology problem

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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topChow, Sum S., Carey, Graham F., and Anderson, Michael L.. "Finite element approximations of a glaciology problem." ESAIM: Mathematical Modelling and Numerical Analysis 38.5 (2010): 741-756. <http://eudml.org/doc/194237>.

@article{Chow2010,

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.
},

author = {Chow, Sum S., Carey, Graham F., Anderson, Michael L.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Glen's flow law; non-Newtonian fluids; finite element
error estimates; successive approximations.},

language = {eng},

month = {3},

number = {5},

pages = {741-756},

publisher = {EDP Sciences},

title = {Finite element approximations of a glaciology problem},

url = {http://eudml.org/doc/194237},

volume = {38},

year = {2010},

}

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

DA - 2010/3//

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: 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.

LA - eng

KW - Glen's flow law; non-Newtonian fluids; finite element
error estimates; successive approximations.

UR - http://eudml.org/doc/194237

ER -

## References

top- H. Blatter, Velocity and stress fields in grounded glaciers: A simple algorithm for including deviatoric stress gradients. J. Glaciology41 (1995) 333–344.
- G.F. Carey, Computational Grids: Generation, Adaptation and Solution Strategies. Taylor & Francis (1997).
- S.-S. Chow, Finite element error estimates for nonlinear elliptic equations of monotone type. Numer. Math.54 (1989) 373–393.
- S.-S. Chow, Finite element error estimates for a blast furnace gas flow problem. SIAM J. Numer. Analysis29 (1992) 769–780.
- S.-S. Chow and G.F. Carey, Numerical approximation of generalized Newtonian fluids using Heindl elements: I. Theoretical estimates. Internat. J. Numer. Methods Fluids41 (2003) 1085–1118.
- J. Colinge and H. Blatter, Stress and velocity fields in glaciers: Part I. Finite-difference schemes for higher-order glacier models. J. Glaciology44 (1998) 448–456.
- J. Colinge and J. Rappaz, A strongly nonlinear problem arising in glaciology. ESAIM: M2AN33 (1999) 395–406.
- 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.
- R. Glowinski and J. Rappaz, Approximation of a nonlinear elliptic problem arising in a non-Newtonian fluid flow model in glaciology. ESAIM: M2AN37 (2003) 175–186.
- W. Han, J. Soren and I. Shimansky, The Kačanov method for some nonlinear problems. Appl. Num. Anal.24 (1997) 57–79.
- C. Johnson and V. Thomee, Error estimates for a finite element approximation of a minimal surface. Math. Comp.29 (1975) 343–349.
- W.B. Liu and J.W. Barrett, Finite element approximation of some degenerate monotone quasilinear elliptic systems. SIAM J. Numer. Analysis33 (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).

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