From a cell model with active motion to a Hele–Shaw-like system: a numerical approach
In this paper we deal with the numerical solution of a Hele{Shaw-like system via a cell model with active motion. Convergence of approximations is established for well-posed initial data. These data are chosen in such a way the time derivate is positive at the initial time. The numerical method is c...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/89743 |
| Acceso en línea: | https://hdl.handle.net/11441/89743 https://doi.org/10.1007/s00211-019-01053-7 |
| Access Level: | acceso abierto |
| Palabra clave: | Finite-element approximation Nonlinear diffusion Free boundary problems Hele-Shaw flows |
| Sumario: | In this paper we deal with the numerical solution of a Hele{Shaw-like system via a cell model with active motion. Convergence of approximations is established for well-posed initial data. These data are chosen in such a way the time derivate is positive at the initial time. The numerical method is constructed by means of a nite element procedure together with the use of a closed-nodal integration. This gives rise to an algorithm which preserves positivity whenever a right-angled triangulation is considered. As a result, uniform-in-time a priori estimates are proven which allows us to pass to limit towards a solution to the Hele{Shaw problem. |
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