Nitsche's method for the stationary Boussinesq system under mixed and nonlinear boundary conditions
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917389826785280 |
|---|---|
| author | Bansal, Aparna Barnafi, Nicolás A. Sperone, Gianmarco Pandey, Dwijendra N. |
| author_facet | Bansal, Aparna Barnafi, Nicolás A. Sperone, Gianmarco Pandey, Dwijendra N. |
| contents | In this paper we analyze Nitsche's method for the stationary Boussinesq system with Navier's slip and a nonlinear boundary condition. Our analysis of the formulation establishes the robustness of a finite elements scheme in arbitrarily complex boundaries. The well-posedness of the discrete problem is established using fixed-point theorems under a standard smallness assumption on the data. We also provide optimal convergence rates for the approximation error. Furthermore, the efficiency and reliability of residual-based a posteriori error estimators are established. We validate our theory through several numerical tests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06560 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nitsche's method for the stationary Boussinesq system under mixed and nonlinear boundary conditions Bansal, Aparna Barnafi, Nicolás A. Sperone, Gianmarco Pandey, Dwijendra N. Numerical Analysis 65N30, 65N12, 65N15, 65J15, 76D05 In this paper we analyze Nitsche's method for the stationary Boussinesq system with Navier's slip and a nonlinear boundary condition. Our analysis of the formulation establishes the robustness of a finite elements scheme in arbitrarily complex boundaries. The well-posedness of the discrete problem is established using fixed-point theorems under a standard smallness assumption on the data. We also provide optimal convergence rates for the approximation error. Furthermore, the efficiency and reliability of residual-based a posteriori error estimators are established. We validate our theory through several numerical tests. |
| title | Nitsche's method for the stationary Boussinesq system under mixed and nonlinear boundary conditions |
| topic | Numerical Analysis 65N30, 65N12, 65N15, 65J15, 76D05 |
| url | https://arxiv.org/abs/2604.06560 |