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

 

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Opened Access On the stability of approximations for the Stokes problem using different finite element spaces for each component of the velocity
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Author: Guillén González, Francisco Manuel
Rodríguez Galván, José Rafael
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2016-01
Published in: Applied Numerical Mathematics, 99, 51-76.
Document type: Article
Abstract: 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.
Cite: Guillén González, F.M. y Rodríguez Galván, J.R. (2016). On the stability of approximations for the Stokes problem using different finite element spaces for each component of the velocity. Applied Numerical Mathematics, 99, 51-76.
Size: 2.647Mb
Format: PDF

URI: http://hdl.handle.net/11441/42873

DOI: 10.1016/j.apnum.2015.07.002

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