Genming Bai : Fast algorithms and numerical analysis for geometric flows and curvature-driven interface problems

Speaker
Genming Bai, University of Michigan, Ann Arbor

Abstract
In this talk, we present our recent major progress in parametric finite element methods by providing the first-ever convergence proof for an iso-parametric finite element discretization of two-phase Stokes flow in $\Omega \subset \mathbb{R}^d$, $d=2,3$, with interface dynamics governed by mean curvature.
The proof relies on a crucial discrete coupled parabolicity structure of the error system and a powerful iso-parametric framework of convergence analysis where we do not really discriminate consistency and stability.
We will also introduce a conservative fast spectral method incorporating tangential smoothing velocity.
Applications to biological vesicles (e.g. red blood cells) will be demonstrated as well.
The methodologies and treatments developed in this series of works are hopeful to become standard in the future.