Steady, Shallow Ice Sheets as Obstacle Problems: Well-Posedness and Finite Element Approximation

@article{Jouvet2012SteadySI,
title={Steady, Shallow Ice Sheets as Obstacle Problems: Well-Posedness and Finite Element Approximation},
author={Guillaume Jouvet and Ed Bueler},
journal={SIAM Journal of Applied Mathematics},
year={2012},
volume={72},
pages={1292-1314}
}

We formulate steady, shallow ice sheet flow as an obstacle problem, the unknown being the ice upper surface and the obstacle being the underlying bedrock topography. This generates a free-boundary defining the ice sheet extent. The obstacle problem is written as a variational inequality subject to the positive-ice-thickness constraint. The corresponding PDE is a highly nonlinear elliptic equation which generalizes the p-Laplacian equation. Our formulation also permits variable ice softness… CONTINUE READING