Josefin Ahlkrona: Local Projection Stabilisation of the p-Stokes Equations on Anisotropic Meshes - Motivated by Ice Sheet Modelling

Abstract:

The p-Stokes equations describes non-Newtonian fluid flow. In many industrial applications and natural settings such non-Newtonian flow takes place in flat domains, so that anisotropic are needed. In the first part of this talk an a-priori analysis of an equal order bi-linear finite element discretisation with a modified Local Projection Stabilisation is presented. The results suggest that the non-linear problem amplifies the effect of the anisotropy. Some numerical experiments are presented and possible alterations of the stabilisation term are discussed.

The work presented in the first part was initiated with the hope of improving the stability of ice sheet simulations. The melting of the Greenland and Antarctic Ice Sheet is crucial to understand in order to estimate future sea-level rise and climate. Modelling of ice sheets offers many interesting and challenging numerical issues. In the second part of the talk, an introduction to ice sheet modelling is given, and stability and efficiency issues are explored.