Approximation of a nonlinear elliptic problem arising in a non-Newtonian fluid flow model in glaciology. (English) Zbl 1046.76002

Glowinski, Roland; Rappaz, Jacques

M2AN, Math. Model. Numer. Anal. 37, No. 1, 175-186 (2003).

Summary: The goal is to establish a priori and a posteriori error estimates for numerical approximations of some nonlinear 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 obtained theoretical results are almost optimal.

MSC:

76A05	Non-Newtonian fluids
76M10	Finite element methods applied to problems in fluid mechanics
65N15	Error bounds for boundary value problems involving PDEs
86A40	Glaciology

Keywords:

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

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