## The Monolithic Arbitrary Lagrangian-Eulerian (ALE) Finite Element Analysis of Moving Interface Problems

#### Speaker: Rihui Lan (University of South Carolina)

In this talk, two different moving interface problems are studied by different arbitrary Lagrangian-Eulerian (ALE) finite element methods. For the transient Stokes/parabolic coupling with jump coefficients—a linearized fluid-structure interaction (FSI) problem, a novel $$H^1$$-projection is defined to account for the mesh motion. The well-posedness and optimal convergence properties in both the energy norm and $$L^2$$ norm are analyzed for this mixed-type $$H^1$$-projection, with which the stability and optimal error estimate in the energy norm are derived for both semi- and fully discrete mixed finite element approximations to the Stokes/parabolic interface problem. For the parabolic/mixed parabolic moving interface problem with jump coefficients, a stable Stokes-pair mixed FEM within a specific stabilization technique and a novel ALE time-difference scheme are developed to discretize this interface problem in both semi- and fully discrete fashion, for which the stability and optimal error estimate analyses are conducted.

Time: March 27, 2020 2:30pm-3:30pm October 2, 2020 2:30pm-3:30pm
Location: LC317R Virtually via Zoom
Host: Lili Ju