The main goal of this article is to establish a priori and a posteriori error estimates for the numerical approximation of some non linear elliptic problems arising in glaciology. The stationary motion of a glacier is given by a non-newtonian fluid flow model which becomes, in a first two-dimensional approximation, the so-called infinite parallel sided slab model. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1. Numerical results show that the theoretical results we have obtained are almost optimal.
Mots clés : finite element method, a priori error estimates, a posteriori error estimates, non-newtonian fluids, infinite parallel sided slab model in glaciology
@article{M2AN_2003__37_1_175_0,
author = {Glowinski, Roland and Rappaz, Jacques},
title = {Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {175--186},
publisher = {EDP-Sciences},
volume = {37},
number = {1},
year = {2003},
doi = {10.1051/m2an:2003012},
mrnumber = {1972657},
zbl = {1046.76002},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2003012/}
}
TY - JOUR AU - Glowinski, Roland AU - Rappaz, Jacques TI - Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 175 EP - 186 VL - 37 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2003012/ DO - 10.1051/m2an:2003012 LA - en ID - M2AN_2003__37_1_175_0 ER -
%0 Journal Article %A Glowinski, Roland %A Rappaz, Jacques %T Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 175-186 %V 37 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2003012/ %R 10.1051/m2an:2003012 %G en %F M2AN_2003__37_1_175_0
Glowinski, Roland; Rappaz, Jacques. Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 1, pp. 175-186. doi : 10.1051/m2an:2003012. http://archive.numdam.org/articles/10.1051/m2an:2003012/
[1] and. Estimateurs a posteriori d'erreurs pour le calcul adaptatif d'écoulements quasi-newtoniens. RAIRO Modél. Math. Anal. Numér. 25 (1991) 31-48. | Numdam | Zbl
[2] and, Finite element approximation of degenerate quasi-linear elliptic and parabolic problems. Pitman Res. Notes Math. Ser. 303 (1994) 1-16. In Numerical Analysis 1993. | Zbl
[3] , Velocity and stress fields in grounded glacier: a simple algorithm for including deviator stress gradients. J. Glaciol. 41 (1995) 333-344.
[4] , The finite element method for elliptic problems. North-Holland, Stud. Math. Appl. 4 (1978). | MR | Zbl
[5] and, A strongly non linear problem arising in glaciology. ESAIM: M2AN 33 (1999) 395-406. | Numdam | Zbl
[6] and, Sur l'approximation par éléments finis d'ordre un, et la résolution par pénalisation-dualité, d'une classe de problèmes de Dirichlet non linéaires. Anal. Numér. 2 (1975) 41-76. | Numdam | Zbl
[7] ,, and, The blocking of an inhomogeneous Bingham fluid. Applications to landslides. ESAIM: M2AN 36 (2002) 1013-1026. | Numdam | Zbl
[8] and. Quasi-norm local error estimators for -Laplacian. SIAM J. Numer. Anal. 39 (2001) 100-127. | Zbl
[9] , Résolution numérique d'un problème à frontière libre issu de la glaciologie. Diploma thesis, Department of Mathematics, EPFL, Lausanne, Switzerland (2001).
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