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

Roland Glowinski; Jacques Rappaz

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 37.1 (2010): 175-186. <http://eudml.org/doc/194152>.

@article{Glowinski2010,

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.
},

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

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

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

language = {eng},

month = {3},

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/194152},

volume = {37},

year = {2010},

}

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

DA - 2010/3//

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.; finite element method; a priori error estimates; a posteriori error estimates

UR - http://eudml.org/doc/194152

ER -

## References

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- 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.
- H. Blatter, Velocity and stress fields in grounded glacier: a simple algorithm for including deviator stress gradients. J. Glaciol.41 (1995) 333-344.
- P.G. Ciarlet, The finite element method for elliptic problems. North-Holland, Stud. Math. Appl. 4 (1978).
- J. Colinge and J. Rappaz, A strongly non linear problem arising in glaciology. ESAIM: M2AN33 (1999) 395-406.
- 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.
- P. Hild, I.R. Ionescu, T. Lachand-Robert and I. Rosca, The blocking of an inhomogeneous Bingham fluid. Applications to landslides. ESAIM: M2AN36 (2002) 1013-1026.
- W. Liu and N. Yan. Quasi-norm local error estimators for p-Laplacian. SIAM J. Numer. Anal. 39 (2001) 100-127.
- A. Reist, Résolution numérique d'un problème à frontière libre issu de la glaciologie. Diploma thesis, Department of Mathematics, EPFL, Lausanne, Switzerland (2001).

## Citations in EuDML Documents

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- Marco Picasso, Jacques Rappaz, Adrian Reist, Numerical simulation of the motion of a three-dimensional glacier
- Sum S. Chow, Graham F. Carey, Michael L. Anderson, Finite element approximations of a glaciology problem
- Boris Andreianov, Franck Boyer, Florence Hubert, Finite volume schemes for the p-laplacian on cartesian meshes
- Boris Andreianov, Franck Boyer, Florence Hubert, Finite volume schemes for the p-Laplacian on Cartesian meshes
- Jérôme Droniou, Finite volume schemes for fully non-linear elliptic equations in divergence form
- Jérôme Droniou, Finite volume schemes for fully non-linear elliptic equations in divergence form

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