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Predicting the evolution of ice sheets requires numerical models ableto accurately track the migration of ice sheet continental margins orgrounding lines. We introduce a physically based moving-point approachfor the flow of ice sheets based on the conservation of localmasses. This allows the ice sheet margins to be tracked explicitly. Our approach is also well suited to capture waiting-time behaviour efficiently.A finite-difference moving-point scheme is derived and applied in a simplifiedcontext (continental radially symmetrical shallow iceapproximation). The scheme, which is inexpensive, is verified by comparing the results with steady states obtained from an analytic solution and with exact moving-margin transient solutions.In both cases the scheme is able to track the position of theice sheet margin with high accuracy

A moving-point approach to model shallow ice sheets: a study case with radially symmetrical ice sheets