A reduced discrete inf-sup condition in Lp for incompressible flows and application

In this work, we introduce a discrete specific inf-sup condition to estimate the Lp norm, 1 <p< +∞, of the pressure in a number of fluid flows. It applies to projection-based stabilized finite element discretizations of incompressible flows, typically when the velocity field has a low regulari...

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Detalhes bibliográficos
Autores: Chacón Rebollo, Tomás, Girault, Vivette, Gómez Mármol, María Macarena, Sánchez Muñoz, Isabel María
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42896
Acesso em linha:http://hdl.handle.net/11441/42896
https://doi.org/10.1051/m2an/2015008
Access Level:acceso abierto
Palavra-chave:Inf-sup condition
Finite element method
stabilized method
incompressible flows
primitive equations of the Ocean
Descrição
Resumo:In this work, we introduce a discrete specific inf-sup condition to estimate the Lp norm, 1 <p< +∞, of the pressure in a number of fluid flows. It applies to projection-based stabilized finite element discretizations of incompressible flows, typically when the velocity field has a low regularity. We derive two versions of this inf-sup condition: The first one holds on shape-regular meshes and the second one on quasi-uniform meshes. As an application, we derive reduced inf-sup conditions for the linearized Primitive equations of the Ocean that apply to the surface pressure in weighted Lp norm. This allows to prove the stability and convergence of quite general stabilized discretizations of these equations: SUPG, Least Squares, Adjoint-stabilized and OSS discretizations.