Finite element approximations of a glaciology problem
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 741-756.

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.

DOI : 10.1051/m2an:2004033
Classification : 26B25, 35J20, 35J60, 49J45, 65N30, 86A40
Mots-clés : Glen's flow law, non-newtonian fluids, finite element error estimates, successive approximations 
@article{M2AN_2004__38_5_741_0,
     author = {Chow, Sum S. and Carey, Graham F. and Anderson, Michael L.},
     title = {Finite element approximations of a glaciology problem},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {741--756},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {5},
     year = {2004},
     doi = {10.1051/m2an:2004033},
     mrnumber = {2104426},
     zbl = {1130.86300},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an:2004033/}
}
TY  - JOUR
AU  - Chow, Sum S.
AU  - Carey, Graham F.
AU  - Anderson, Michael L.
TI  - Finite element approximations of a glaciology problem
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2004
SP  - 741
EP  - 756
VL  - 38
IS  - 5
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/m2an:2004033/
DO  - 10.1051/m2an:2004033
LA  - en
ID  - M2AN_2004__38_5_741_0
ER  - 
%0 Journal Article
%A Chow, Sum S.
%A Carey, Graham F.
%A Anderson, Michael L.
%T Finite element approximations of a glaciology problem
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2004
%P 741-756
%V 38
%N 5
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/m2an:2004033/
%R 10.1051/m2an:2004033
%G en
%F M2AN_2004__38_5_741_0
Chow, Sum S.; Carey, Graham F.; Anderson, Michael L. Finite element approximations of a glaciology problem. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 741-756. doi : 10.1051/m2an:2004033. http://www.numdam.org/articles/10.1051/m2an:2004033/

[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] G.F. Carey, Computational Grids: Generation, Adaptation and Solution Strategies. Taylor & Francis (1997). | MR | Zbl

[3] S.-S. Chow, Finite element error estimates for nonlinear elliptic equations of monotone type. Numer. Math. 54 (1989) 373-393. | Zbl

[4] S.-S. Chow, Finite element error estimates for a blast furnace gas flow problem. SIAM J. Numer. Analysis 29 (1992) 769-780. | Zbl

[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. | Zbl

[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] J. Colinge and J. Rappaz, A strongly nonlinear problem arising in glaciology. ESAIM: M2AN 33 (1999) 395-406. | Numdam | Zbl

[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] 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. | Numdam | Zbl

[10] W. Han, J. Soren and I. Shimansky, The Kačanov method for some nonlinear problems. Appl. Num. Anal. 24 (1997) 57-79. | Zbl

[11] C. Johnson and V. Thomee, Error estimates for a finite element approximation of a minimal surface. Math. Comp. 29 (1975) 343-349. | Zbl

[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. | Zbl

[13] W.S.B. Patterson, The Physics of Glaciers, 2nd edition. Pergamon Press (1981).

[14] E. Zeidler, Nonlinear Functional Analysis and Its Applications II/B. Nonlinear Monotone Operators, Springer-Verlag (1990). | MR | Zbl

Cité par Sources :