# Accurate and stable time stepping in ice sheet modeling

**Cheng Gong
**

Division of Scientific Computing

Department of Information Technology

Uppsala University

Uppsala

### Abstract:

The efficiency, stability and accuracy are the three major issues in the numerical simulation of paleo ice sheet modeling. We introduce adaptive time step control for simulation of evolution of ice sheets. The discretization error in the approximations is estimated using "Milne's device" by comparing the result from two different methods in a predictor-corrector pair.

The time step is changed in an efficient way such that the velocity field equation is only solved once per time step. The stability of the numerical solution is maintained and the accuracy is controlled by keeping the local error below a given threshold using PI-control.