We are seeking a highly motivated postdoctoral researcher to improve and analyse time-stepping schemes for simulations of glacial ice dynamics. The motivation is the need for more reliable predictions of how ice sheets and glaciers respond to climate change. The project builds on a stabilization method that allows much larger time-steps than previously possible. Thanks to the stabilization, step length is now limited by accuracy rather than numerical stability, but there is still little rigorous understanding of how accuracy depends on time-step size, which varies substantially over the course of a simulation. The project's aim is twofold: to deepen the theoretical understanding of the stabilized scheme, and to translate this understanding into a practical, adaptive algorithm that automatically selects the largest time-step preserving the desired accuracy. The successful candidate will have the opportunity to shape the research direction and contribute both methodologically and computationally.