# Christian Helanow: Finite element approximations of the p-Stokes equations for ice-sheet models

**Time: **
Wed 2020-05-20 14.00 - 14.45

**Lecturer: **
Christian Helanow, Stockholms universitet

**Location: **
Zoom, meeting ID: 619 6390 9394

### Abstract

Ice, when accumulated into large enough masses like glaciers and ice sheets, behaves like a highly viscous and incompressible non-Newtonian fluid. The flow of glaciers is most accurately described by the p-Stokes equations using a power-law to relate stresses to deformation. For glacier-flow models, which often consider large physical domains with complex topography, the Finite Element Method (FEM) is a common choice to approximate the solution of the system. However, the resulting set of equations present numerical challenges. In particular, we have that 1) the saddle-point nature of the p-Stokes equations, due to the "inf-sup" (Babuska-Brezzi) condition, limits the choices of stable finite elements formulations, and 2) the power-law nature of the fluid can result in infinite viscosity in zones of zero deformation, limiting the convergence rate of the discrete solution.

The current study aims to use the theoretical framework of FEM for the p-Stokes equations and numerical experiments to investigate the accuracy of equal-order stabilized finite elements, e.g. Galerkin-Least-Squares, Local Projection and Interior Penalty methods, and compare this inf-sup stable elements that are relatively computationally cheap, e.g. the MINI element.