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On a doubly nonlinear parabolic obstacle problem modelling ice sheet dynamics

Díaz Díaz, Jesús Ildefonso and Calvo, N. and Durany, J. and Schiavi, E. and Vázquez, C. (2002) On a doubly nonlinear parabolic obstacle problem modelling ice sheet dynamics. SIAM Journal on applied mathematics, 63 (2). 683-707 . ISSN 0036-1399

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Abstract

This paper deals with the weak formulation of a free (moving) boundary problem arising in theoretical glaciology. Considering shallow ice sheet flow, we present the mathematical analysis and the numerical solution of the second order nonlinear degenerate parabolic equation modelling, in the isothermal case, the ice sheet non-Newtonian dynamics. An obstacle problem is then deduced and analyzed. The existence of a free boundary generated by the support of the solution is proved and its location and evolution are qualitatively described by using a comparison principle and an energy method. Then the solutions are numerically computed with a method of characteristics and a duality algorithm to deal with the resulting variational inequalities. The weak framework we introduce and its analysis (both qualitative and numerical) are not restricted to the simple physics of the ice sheet model we consider nor to the model dimension; they can be successfully applied to more realistic and sophisticated models related to other geophysical settings.

Item Type:Article
Uncontrolled Keywords:Free boundary; Duality methods; Finite element method; Computational cost reduction; Test examples
Subjects:Sciences > Mathematics > Differential equations
ID Code:12488
Deposited On:28 Mar 2011 14:02
Last Modified:28 Mar 2011 14:02

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