Geoscientific Model Development
Geoscientific Model Development
GMD
Articles | Volume 19, issue 6
Articles | Volume 19, issue 6
https://doi.org/10.5194/gmd-19-2333-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-19-2333-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
Articles | Volume 19, issue 6
Development and technical paper
 | 
23 Mar 2026
Development and technical paper |  | 23 Mar 2026

A fully implicit second order method for viscous free surface Stokes flow – application to glacier simulations

Josefin Ahlkrona, A. Clara J. Henry, and André Löfgren

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Cited articles

Ahlkrona, J., Henry, C., and Löfgren, A.: Code for the publication “A Fully Implicit Second Order Method for Viscous Free Surface Stokes Flow – Application to Glacier Simulations” by Josefin Ahlkrona, André Löfgren and A. Clara J. Henry, Zenodo [code], https://doi.org/10.5281/zenodo.17475634, 2025. a
Amestoy, P., Duff, I. S., Koster, J., and L'Excellent, J.-Y.: A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling, SIAM J. Matrix Anal. Appl., 23, 15–41, https://doi.org/10.1137/S0895479899358194, 2001. a
Andrés-Martínez, M., Morgan, J. P., Pérez-Gussinyé, M., and Rüpke, L.: A new free-surface stabilization algorithm for geodynamical modelling: Theory and numerical tests, Phys. Earth Planet. Inter., 246, 41–51, https://doi.org/10.1016/j.pepi.2015.07.003, 2015. a
Brezzi, F. and Fortin, M.: Mixed and Hybrid Finite Element Methods, Springer-Verlag, Inc., New York, NY, USA, ISBN 0-387-97582-9, 1991. a
Bueler, E.: Stable finite volume element schemes for the shallow-ice Approximation, J. Glaciol., 62, 230–242, https://doi.org/10.1017/jog.2015.3, 2016. a
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This paper leverages the Free Surface Stabilization Algorithm of Kaus et al. (2010) to construct a fully implicit discretization of viscous free surface flows. It also presents the first second order accurate time-stepping scheme applicable to ice sheet models. We test the new method on an idealized problem and on a 2D glacier simulation. The results indicates that the method has great potential to speedup ice sheet models.
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