Analysis and virtual element discretisation of a Stokes/Biot--Kirchhoff bulk--surface model
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911499697520640 |
|---|---|
| author | Dassi, Franco Khot, Rekha Rubiano, Andres E. Ruiz-Baier, Ricardo |
| author_facet | Dassi, Franco Khot, Rekha Rubiano, Andres E. Ruiz-Baier, Ricardo |
| contents | We analyse a coupled 3D-2D model with a free fluid governed by Stokes flow in the bulk and a poroelastic plate described by the Biot-Kirchhoff equations on the surface. Assuming the form of a double perturbed saddle-point problem, the unique solvability of the continuous formulation is proved using Fredholm's theory for compact operators and the Babuska--Brezzi approach for saddle-point problems with penalty. We propose a stable virtual element method, establishing a discrete inf-sup condition under a small mesh assumption through a Fortin interpolant that requires only $H^1$-regularity for the Stokes problem. We show the well-posedness of the monolithic discrete formulation and introduce an equivalent fixed-point approach employed at the implementation level. The optimal convergence of the method in the energy norm is proved theoretically and is also confirmed numerically via computational experiments. We demonstrate an application of the model and the proposed scheme in the simulation of immune isolation using encapsulation with silicon nanopore membranes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis and virtual element discretisation of a Stokes/Biot--Kirchhoff bulk--surface model Dassi, Franco Khot, Rekha Rubiano, Andres E. Ruiz-Baier, Ricardo Numerical Analysis 65N15, 65N99, 74K20, 76D07 We analyse a coupled 3D-2D model with a free fluid governed by Stokes flow in the bulk and a poroelastic plate described by the Biot-Kirchhoff equations on the surface. Assuming the form of a double perturbed saddle-point problem, the unique solvability of the continuous formulation is proved using Fredholm's theory for compact operators and the Babuska--Brezzi approach for saddle-point problems with penalty. We propose a stable virtual element method, establishing a discrete inf-sup condition under a small mesh assumption through a Fortin interpolant that requires only $H^1$-regularity for the Stokes problem. We show the well-posedness of the monolithic discrete formulation and introduce an equivalent fixed-point approach employed at the implementation level. The optimal convergence of the method in the energy norm is proved theoretically and is also confirmed numerically via computational experiments. We demonstrate an application of the model and the proposed scheme in the simulation of immune isolation using encapsulation with silicon nanopore membranes. |
| title | Analysis and virtual element discretisation of a Stokes/Biot--Kirchhoff bulk--surface model |
| topic | Numerical Analysis 65N15, 65N99, 74K20, 76D07 |
| url | https://arxiv.org/abs/2508.02450 |