Modeling the cryosphere with FEniCS

This manuscript is a collection of problems and solutions related to modeling the cryosphere using the finite element software FEniCS. Included is an introduction to the finite element method; solutions to a variety of problems in one, two, and three dimensions; an overview of popular stabilization techniques for numerically-unstable problems; and an introduction to the governing equations of ice-sheet dynamics with associated FEniCS implementations. The software developed for this project, Cryospheric Problem Solver (CSLVR), is fully open-source and has been designed with the goal of simplifying many common tasks associated with modeling the cryosphere. CSLVR possesses the ability to download popular geological and geographical data, easily convert between geographical projections, develop sophisticated two- or three-dimensional finite-element meshes, convert data between many popular formats, and produce production-quality images of data. Scripts are presented which model the flow of ice using geometry defined by mathematical functions and observed Antarctic and Greenland ice-sheets data. A new way of solving the internal energy distribution of ice to match observed intra-ice water contents within temperate regions is thoroughly explained.