Igor Tominec: Stability of the free-surface Stokes problem: time-step restrictions and their improvements

Time stepping for PDEs requires care: the time step size must be small enough to keep the numerical scheme stable. For simple problems, such as the advection or heat equation, the CFL condition tells us how to choose a stable time-step size. For nonlinear systems of PDEs, however, the CFL condition and its analysis framework may not apply. In this talk, I will discuss the nonlinear (non-Newtonian) Stokes problem with a free surface (free boundary), solved using finite elements in space and the explicit Euler method in time. This problem appears in simulations of ice sheets, mantle flow, and lava. I will show you new results on the analysis of the fully discrete stability and how this can be used to derive stabilizations that allow significant improvements of time step sizes.