Stability Analysis of Monolithic Globally Divergence-Free ALE-HDG Methods for Fluid-Structure Interaction
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913014977921024 |
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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 |