A modified Brinkman penalization fictitious domain method for the unsteady Navier-Stokes equations
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_ | 1866909973689139200 |
|---|---|
| author | Baitulenov, Zhanybek Olshanskii, Maxim Temirbekov, Almas Temirbekov, Nurlan Kasenov, Syrym |
| author_facet | Baitulenov, Zhanybek Olshanskii, Maxim Temirbekov, Almas Temirbekov, Nurlan Kasenov, Syrym |
| contents | This paper investigates a modification of the fictitious domain method with continuation in the lower-order coefficients for the unsteady Navier-Stokes equations governing the motion of an incompressible homogeneous fluid in a bounded 2D or 3D domain. The modification enables {a solution-dependent} choice of the critical parameter. Global-in-time existence and convergence of a weak solution to the auxiliary problem are proved, and local-in-time existence and convergence of a unique strong solution are established. For the strong solution, a new higher-order convergence rate estimate in the penalization parameter is obtained. The introduced framework allows us to apply a pointwise divergence free finite element method as a discretization technique, leading to strongly mass conservative discrete fictitious domain method. A numerical example illustrates the performance of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19580 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A modified Brinkman penalization fictitious domain method for the unsteady Navier-Stokes equations Baitulenov, Zhanybek Olshanskii, Maxim Temirbekov, Almas Temirbekov, Nurlan Kasenov, Syrym Numerical Analysis 65M85 This paper investigates a modification of the fictitious domain method with continuation in the lower-order coefficients for the unsteady Navier-Stokes equations governing the motion of an incompressible homogeneous fluid in a bounded 2D or 3D domain. The modification enables {a solution-dependent} choice of the critical parameter. Global-in-time existence and convergence of a weak solution to the auxiliary problem are proved, and local-in-time existence and convergence of a unique strong solution are established. For the strong solution, a new higher-order convergence rate estimate in the penalization parameter is obtained. The introduced framework allows us to apply a pointwise divergence free finite element method as a discretization technique, leading to strongly mass conservative discrete fictitious domain method. A numerical example illustrates the performance of the method. |
| title | A modified Brinkman penalization fictitious domain method for the unsteady Navier-Stokes equations |
| topic | Numerical Analysis 65M85 |
| url | https://arxiv.org/abs/2512.19580 |