Numerical computation of ice sheet profiles with free boundary models

The aim of this work is to develop a numerical method to solve a moving boundary problem governed by a time dependent nonlinear convection-diffusion equation. The mathematical formulation can be framed as a nonlinear parabolic complementarity problem. The model has recently been used to compute ice sheet profiles in theoretical glaciology. After describing the mathematical model of the ice sheet motion and the corresponding dimensionless equations, the proposed numerical method involves an upwind scheme for time semidiscretization, fixed point method for the nonlinear diffusion term, finite elements approximation in space and a duality type algorithm for solving the obstacle like problem at each step. Finally, several numerical simulation examples involving real data sets issued from the Antarctic ice sheet are shown.