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

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

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Autor: Chacón Rebollo, Tomás
Girault, Vivette
Gómez Mármol, María Macarena
Sánchez Muñoz, Isabel María
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2015
Publicado en: ESAIM: Mathematical Modelling and Numerical Analysis, 49, 1219-1238.
Tipo de documento: Artículo
Resumen: 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.
Cita: Chacón Rebollo, T., Girault, V., Gómez Mármol, M.M. y Sánchez Muñoz, I.M. (2015). A reduced discrete inf-sup condition in Lp for incompressible flows and application. ESAIM: Mathematical Modelling and Numerical Analysis, 49, 1219-1238.
Tamaño: 326.0Kb
Formato: PDF

URI: http://hdl.handle.net/11441/42896

DOI: http://dx.doi.org/10.1051/m2an/2015008

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