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

摘要

We investigate the accuracy and robustness of one of the most common methodsused in glaciology for the discretization of the $mathfrak{p}$-Stokesequations: equal order finite elements with Galerkin Least-Squares (GLS)stabilization. Furthermore we compare the results to other stabilized methods.We find that the vertical velocity component is more sensitive to the choice ofGLS stabilization parameter than horizontal velocity. Additionally, theaccuracy of the vertical velocity component is especially important sinceerrors in this component can cause ice surface instabilities and propagate intofuture ice volume predictions. If the element cell size is set to the minimumedge length and the stabilization parameter is allowed to vary non-linearlywith viscosity, the GLS stabilization parameter found in literature is a goodchoice on simple domains. However, near ice margins the standard parameterchoice may result in significant oscillations in the vertical component of thesurface velocity. For these cases, other stabilization techniques, such as theinterior penalty method, result in better accuracy and are less sensitive tothe choice of the stabilization parameter. During this work we also discoveredthat the manufactured solutions often used to evaluate errors in glaciology arenot reliable due to high artificial surface forces at singularities. We performour numerical experiments in both FEniCS and Elmer/Ice.