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...

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Detalles Bibliográficos
Autores: Guillén González, Francisco Manuel, Gutiérrez Santacreu, Juan Vicente
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
Descripción
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.