Compatible Finite Elements for Glacier Modeling

Described in this article is the first application of two mixed finite-element methods to the equations of glacier evolution under different simplifying assumptions, along with a framework for the implicit solution of the coupled velocity-thickness equations. The first method uses Raviartâ€Â"Thomas elements for velocity and piecewise constants for thickness and is a reframing of a classic staggered-grid finite-difference method to the case of unstructured triangular meshes. The second method uses Mardalâ€Â"Taiâ€Â"Winther elements for velocity and exhibits several desirable properties: second-order convergence of velocity and near-exact mass conservation while resolving both membrane and shear stresses in steep topography with thin ice.