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Mechanical error estimators for shallow ice flow models

Published online by Cambridge University Press:  18 October 2016

G. Jouvet
G. Jouvet*
Affiliation:
ETH Zürich, VAW, Hönggerbergring 26, 8093 Zürich, Switzerland
*
†Email address for correspondence: [email protected]
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Abstract

We develop a posteriori ‘mechanical’ error estimators that are able to evaluate the solution discrepancy between two ice flow models. We first reformulate the classical shallow ice flow models by applying simplifications to the weak formulation of the Glen–Stokes model. This approach leads to a unified hierarchical formulation which relates the Glen–Stokes model, the Blatter model, the shallow ice approximation and the shallow shelf approximation. Based on this formulation and on residual techniques commonly used to estimate numerical errors, we derive three a posteriori estimators, each of which compares a pair of models using measures of the velocity field from the simpler (shallower) model. Numerical experiments confirm that these estimators can be used to assess the validity of the shallow ice models that are commonly used in glacier and ice sheet modelling.

JFM classification

Geophysical and Geological Flows: Ice sheets Non-Newtonian Flows: Non-Newtonian Flows Mathematical Foundations: Variational methods
Type
Papers
Information
Journal of Fluid Mechanics , Volume 807 , 25 November 2016 , pp. 40 - 61
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Copyright
© 2016 Cambridge University Press 

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