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math.NA2025
Free-surface Stokes problem: stability estimates and time-step improvements
Igor Tominec, Lukas Lundgren, André Löfgren +2
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In…
math.NA2025
Well-posedness of the Stokes problem under modified pressure Dirichlet boundary conditions
Igor Tominec, Josefin Ahlkrona, Malte Braack
This paper shows that the Stokes problem is well-posed when velocity and pressure simultaneously vanish on the domain boundary. This result is achieved by extending NeÄas' inequal…
math.NA2024
Weak form Shallow Ice Approximation models with an improved time step restriction
Igor Tominec, Josefin Ahlkrona
The Shallow Ice Approximation (SIA) model on strong form is commonly used for inferring the flow dynamics of grounded ice sheets. The solution to the SIA model is a closed-form exp…