On the stability of approximations for the Stokes problem using different finite element spaces for each component of the velocity

This paper studies the stability of velocity-pressure mixed approximations of the Stokes problem when different finite element (FE) spaces for each component of the velocity field are considered. We consider some new combinations of continuous FE reducing the number of degrees of freedom in some vel...

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Detalles Bibliográficos
Autores: Guillén González, Francisco Manuel, Rodríguez Galván, José Rafael
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42873
Acceso en línea:http://hdl.handle.net/11441/42873
https://doi.org/10.1016/j.apnum.2015.07.002
Access Level:acceso abierto
Palabra clave:inf-sup condition
incompressible fluids
mixed variational formulations
finite elements
macro-element technique
Descripción
Sumario:This paper studies the stability of velocity-pressure mixed approximations of the Stokes problem when different finite element (FE) spaces for each component of the velocity field are considered. We consider some new combinations of continuous FE reducing the number of degrees of freedom in some velocity components. Although the resulting FE combinations are not stable in general, by using the Stenberg’s macro-element technique, we show their stability in a wide family of meshes (namely, in uniformly unstructured meshes). Moreover, a post-processing is given in order to convert any mesh family in an uniformly unstructured mesh family. Finally, some 2D and 3D numerical simulations are provided agree with the previous analysis.