Stability Analysis of Monolithic Globally Divergence-Free ALE-HDG Methods for Fluid-Structure Interaction

Organizer：

苏春梅

Speaker：

Xiaoping Xie 谢小平

四川大学

Time：

Wed., 10:00 - 11:00 am

Dec. 17, 2025

Venue：

C548, Shuangqing Complex Building

Title:

Stability Analysis of Monolithic Globally Divergence-Free ALE-HDG Methods for Fluid-Structure Interaction

Abstract:

We propose two monolithic finite element schemes for fluid-structure interaction (FSI) based on the Piola-type Arbitrary Lagrangian-Eulerian (ALE) mapping, where the backward Euler method is applied for the temporal discretization, HDG methods are adopted for the spatial discretization of the incompressible Navier-Stokes equations and the linear elasticity equations, and a continuous Galerkin method is used to solve the mesh movement equation. We derive stability results for both the semi-discrete and fully discrete schemes, and show that the fully discrete velocity approximation is globally divergence-free. Numerical experiments demonstrate the effectiveness of the proposed methods.