Jouvet, G. and Bueler, E. (2012) Steady, shallow ice sheets as obstacle problems: Wellposedness and finite element approximation. SIAM J. Appl. Math., 72 (4). pp. 12921314. ISSN 00361399

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Official URL: https://dx.doi.org/10.1137/110856654
Abstract
We formulate steady, shallow ice sheet flow as an obstacle problem, the unknown being the ice upper surface and the obstacle being the underlying bedrock topography. This generates a freeboundary defining the ice sheet extent. The obstacle problem is written as a variational inequality subject to the positiveicethickness constraint. The corresponding PDE is a highly nonlinear elliptic equation which generalizes the $p$Laplacian equation. Our formulation also permits variable ice softness, basal sliding, and elevationdependent surface mass balance. Existence and uniqueness are shown in restricted cases which we may reformulate as a convex minimization problem. In the general case we show existence by applying a fixed point argument. Using continuity results from that argument, we construct a numerical solution by solving a sequence of obstacle $p$Laplacianlike problems by finite element approximation. As a real application, we compute the steadystate shape of the Greenland ice sheet in a steady presentday climate.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  1867 
Deposited By:  Ekaterina Engel 
Deposited On:  13 Apr 2016 09:06 
Last Modified:  03 Mar 2017 14:42 
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