# Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology

Roland Glowinski; Jacques Rappaz^{[1]}

- [1] Ecole Polytechnique Federale Institute of Analysis and Scientific Computing CH-1015 Lausanne Switzerland

- Volume: 37, Issue: 1, page 175-186
- ISSN: 0764-583X

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topGlowinski, Roland, and Rappaz, Jacques. "Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.1 (2003): 175-186. <http://eudml.org/doc/245586>.

@article{Glowinski2003,

abstract = {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.},

affiliation = {Ecole Polytechnique Federale Institute of Analysis and Scientific Computing CH-1015 Lausanne Switzerland},

author = {Glowinski, Roland, Rappaz, Jacques},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {finite element method; a priori error estimates; a posteriori error estimates; non-newtonian fluids; infinite parallel sided slab model in glaciology},

language = {eng},

number = {1},

pages = {175-186},

publisher = {EDP-Sciences},

title = {Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology},

url = {http://eudml.org/doc/245586},

volume = {37},

year = {2003},

}

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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2003

PB - EDP-Sciences

VL - 37

IS - 1

SP - 175

EP - 186

AB - 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.

LA - eng

KW - finite element method; a priori error estimates; a posteriori error estimates; non-newtonian fluids; infinite parallel sided slab model in glaciology

UR - http://eudml.org/doc/245586

ER -

## References

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- [5] J. Colinge and J. Rappaz, A strongly non linear problem arising in glaciology. ESAIM: M2AN 33 (1999) 395–406. Zbl0946.65115
- [6] R. Glowinski and A. Marrocco, 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. Zbl0368.65053
- [7] P. Hild, I.R. Ionescu, T. Lachand-Robert and I. Rosca, The blocking of an inhomogeneous Bingham fluid. Applications to landslides. ESAIM: M2AN 36 (2002) 1013–1026. Zbl1057.76004
- [8] W. Liu and N. Yan. Quasi-norm local error estimators for $p$-Laplacian. SIAM J. Numer. Anal. 39 (2001) 100–127. Zbl1001.65119
- [9] A. Reist, 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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