Journal Article

A coupled multivalued model for ice streams and its numerical simulation

Nati Calvo, José Durany, Ana I. Muñoz, Emanuele Schiavi and Carlos Vázquez

in IMA Journal of Applied Mathematics

Published on behalf of Institute of Mathematics and its Applications

Volume 71, issue 1, pages 62-91
Published in print February 2006 | ISSN: 0272-4960
Published online February 2006 | e-ISSN: 1464-3634 | DOI:
A coupled multivalued model for ice streams and its numerical simulation

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This paper deals with the numerical solution of a non-linear model describing a free-boundary problem arising in modern glaciology. Considering a shallow, viscous ice sheet flow along a soft, deformable bed, a coupled non-linear system of differential equations can be obtained. Particularly, an obstacle problem is then deduced and solved in the framework of its complementarity formulation. We present the numerical solution of the resulting multivalued system modelling the ice sheet non-Newtonian dynamics driven by the underlying drainage system. Our numerical results show the existence of fast ice streams when positive wave-like initial conditions are considered. The solutions are numerically computed with a decoupling iterative method and finite-element technique. A duality algorithm and a projected Gauss–Seidel method are the alternatives used to cope with the resulting variational inequality while the explicit treatment, Newton method or a duality method are proposed to deal with the non-linear source term. Finally, the numerical solutions are physically interpreted and some comparisons among the numerical methods are then discussed.

Keywords: ice sheet models; free boundaries; weak solutions; characteristics method; finite elements; duality methods

Journal Article.  0 words. 

Subjects: Applied Mathematics

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