Computational Geosciences

, Volume 22, Issue 4, pp 951–974 | Cite as

Stabilized equal low-order finite elements in ice sheet modeling – accuracy and robustness

  • Christian HelanowEmail author
  • Josefin Ahlkrona
Open Access
Original Paper


We investigate the accuracy and robustness of one of the most common methods used in glaciology for finite element discretization of the 𝔭-Stokes equations: linear equal order finite elements with Galerkin least-squares (GLS) stabilization on anisotropic meshes. Furthermore, we compare the results to other stabilized methods. We find that the vertical velocity component is more sensitive to the choice of GLS stabilization parameter than horizontal velocity. Additionally, the accuracy of the vertical velocity component is especially important since errors in this component can cause ice surface instabilities and propagate into future ice volume predictions. If the element cell size is set to the minimum edge length and the stabilization parameter is allowed to vary non-linearly with viscosity, the GLS stabilization parameter found in literature is a good choice on simple domains. However, near ice margins the standard parameter choice may result in significant oscillations in the vertical component of the surface velocity. For these reasons, other stabilization techniques, in particular the interior penalty method, result in better accuracy and are less sensitive to the choice of stabilization parameter. During this work, we also discovered that the manufactured solutions often used to evaluate errors in glaciology are not reliable due to high artificial surface forces at singularities. We perform our numerical experiments in both FEniCS and Elmer/Ice.


Finite element method Galerkin least-squares p-Stokes Ice-sheet modeling Anisotropic mesh 

Mathematics Subject Classification 2010

76M10 86A40 76A05 76A20 



Christian Helanow was supported by the nuclear waste management organizations in Sweden (Svensk Kärnbränslehantering AB) and Finland (Posiva Oy) through the Greenland Analogue Project and by Gålöstiftelsen. Josefin Ahlkrona was supported by the Swedish strategic research programme eSSENCE (Uppsala) and the cluster of Excellence 80 “The Future Ocean” (Kiel). The “Future Ocean” is funded within the framework of the Excellence Initiative by the Deutsche Forschungsgemeinschaft (DFG) on behalf of the German federal and state governments. The computations with Elmer/Ice were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at PDC Centre for High Performance Computing (PDC-HPC) and at Uppmax at Uppsala University. Both facilities provided excellent support. We wish to thank two anonymous reviewers for their constructive criticism, and Per Lötstedt and Peter Jansson for valuable comments on the manuscript.


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Authors and Affiliations

  1. 1.Department of Physical GeographyStockholm UniversityStockholmSweden
  2. 2.Division of Scientific Computing, Department of Information TechnologyUppsala UniversityUppsalaSweden
  3. 3.The Mathematical SeminarUniversity of KielKielGermany

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