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

 

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Opened Access A reduced discrete inf-sup condition in Lp for incompressible flows and application
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Author: Chacón Rebollo, Tomás
Girault, Vivette
Gómez Mármol, María Macarena
Sánchez Muñoz, Isabel María
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2015
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, 49, 1219-1238.
Document type: Article
Abstract: 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.
Cite: 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.
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URI: http://hdl.handle.net/11441/42896

DOI: 10.1051/m2an/2015008

This work is under a Creative Commons License: 
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