Josefin Ahlkrona, Christian Helanow, Malte Braack
Math. Seminar, Christian-Albrechts-Universität, Kiel, Germany
Ice Sheet Models simulates the deformation of the ice in e.g. the Greenland or the Antarctic Ice Sheet. The most sophisticated ice sheet models solves the p-Stokes equations for the velocity and pressure, coupled to an advection equation describing the position of the ice sheet surface. Such models are capable of modelling fast flowing regions near the coast lines; regions that are currently losing mass rapidly. Unfortunately these models are also prone to instabilities, often rendering long term accurate simulations unfeasible. We take a closer look at these instabilities in two different finite element ice sheet models. We study how the non-linear material properties and thin domains associated with ice sheets affect the errors, we compare common stabilisation technique, and derive a priori error estimates for a specialised discretization.