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

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

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

Abstract

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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.

How to cite

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Glowinski, 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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  1. [1] J. Baranger and H. El Amri. Estimateurs a posteriori d’erreurs pour le calcul adaptatif d’écoulements quasi-newtoniens. RAIRO Modél. Math. Anal. Numér. 25 (1991) 31–48. Zbl0712.76068
  2. [2] J.W. Barrett and W. Liu, Finite element approximation of degenerate quasi-linear elliptic and parabolic problems. Pitman Res. Notes Math. Ser. 303 (1994) 1–16. In Numerical Analysis 1993. Zbl0798.65092
  3. [3] H. Blatter, Velocity and stress fields in grounded glacier: a simple algorithm for including deviator stress gradients. J. Glaciol. 41 (1995) 333–344. 
  4. [4] P.G. Ciarlet, The finite element method for elliptic problems. North-Holland, Stud. Math. Appl. 4 (1978). Zbl0383.65058MR520174
  5. [5] J. Colinge and J. Rappaz, A strongly non linear problem arising in glaciology. ESAIM: M2AN 33 (1999) 395–406. Zbl0946.65115
  6. [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. [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. [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. [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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