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Main Authors: Liu, Shuaijun, Xie, Xiaoping
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.27594
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author Liu, Shuaijun
Xie, Xiaoping
author_facet Liu, Shuaijun
Xie, Xiaoping
contents In this paper, we propose two monolithic fully discrete finite element methods for fluid-structure interaction (FSI) based on a novel Piola-type Arbitrary Lagrangian-Eulerian (ALE) mapping. For the temporal discretization, we apply the backward Euler method to both the non-conservative and conservative formulations. For the spatial discretization, we adopt arbitrary order hybridizable discontinuous Galerkin (HDG) methods for the incompressible Navier-Stokes and linear elasticity equations, and a continuous Galerkin (CG) method for the fluid mesh movement. We derive stability results for both the temporal semi-discretization and the fully discretization, and show that the velocity approximations of the fully discrete schemes are globally divergence-free. Several numerical experiments are performed to verify the performance of the proposed methods.
format Preprint
id arxiv_https___arxiv_org_abs_2603_27594
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Stability Analysis of Monolithic Globally Divergence-Free ALE-HDG Methods for Fluid-Structure Interaction
Liu, Shuaijun
Xie, Xiaoping
Numerical Analysis
In this paper, we propose two monolithic fully discrete finite element methods for fluid-structure interaction (FSI) based on a novel Piola-type Arbitrary Lagrangian-Eulerian (ALE) mapping. For the temporal discretization, we apply the backward Euler method to both the non-conservative and conservative formulations. For the spatial discretization, we adopt arbitrary order hybridizable discontinuous Galerkin (HDG) methods for the incompressible Navier-Stokes and linear elasticity equations, and a continuous Galerkin (CG) method for the fluid mesh movement. We derive stability results for both the temporal semi-discretization and the fully discretization, and show that the velocity approximations of the fully discrete schemes are globally divergence-free. Several numerical experiments are performed to verify the performance of the proposed methods.
title Stability Analysis of Monolithic Globally Divergence-Free ALE-HDG Methods for Fluid-Structure Interaction
topic Numerical Analysis
url https://arxiv.org/abs/2603.27594