Abstract
We investigate the accuracy and robustness of one of the most common methods used in glaciology for finite element discretization of the \U0001d52d-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.
Highlights
Ice sheets and glaciers are important components of the climate system
We investigate how the errors influence the accuracy of ice surface position calculations and how they depend on the Galerkin least-squares (GLS) stabilization parameter, as it is currently not clear how numerical errors resulting from solving the discretized p-Stokes system interplay with the simulations of the ice surface evolution and, predictions of future ice volume
Choosing a sub-optimal value for the stabilization parameter can affect the accuracy of the solution, which can have a negative effect when coupled to other numerical models of for instance the evolution of the free surface or the subglacial hydrological system
Summary
Ice sheets and glaciers are important components of the climate system. Their melting is one of the main sources of sea-level rise [26], and in the past, major climatic events have been triggered by the dynamics of ice sheets [3, 37]. Numerical modeling is a key tool to understand both past and future evolution of ice sheets. The dynamics of ice sheets can be described as a very viscous, incompressible, non-Newtonian free surface, thinfilm flow, driven by gravity. The velocity field and pressure are given by the solution of a non-linear (steady-state) Stokes system – p-Stokes system. The position of the ice-atmosphere interface is computed by solving an additional convection equation where the velocity field enters as coefficients
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