Compatible Finite Elements for Glacier Modeling

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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.




Brinkerhoff, D. J. (2023). Compatible Finite Elements for Glacier Modeling. Computing in Science and Engineering, 25(3), 18–28.

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