Volume 49, Number 4, July-August 2015
|Page(s)||1219 - 1238|
|Published online||06 July 2015|
A reduced discrete inf-sup condition in Lp for incompressible flows and application
Departamento de Ecuaciones Diferenciales y Análisis Numérico and
Instituto de Matemáticas de la Universidad de Sevilla (IMUS),
Apdo. de correos 1160, Universidad de
2 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie & C.N.R.S, UMR 7598, Paris 6, 4 Place Jussieu, 75252 Paris cedex 05, France
3 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Apdo. de correos 1160, Universidad de Sevilla, 41080 Sevilla, Spain
4 Departamento de Matemática Aplicada I, Carretera de Utrera Km 1, Universidad de Sevilla, 41013 Sevilla, Spain
Revised: 15 October 2014
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.
Mathematics Subject Classification: 35Q35 / 65N12 / 76D05
Key words: Inf-sup condition / Finite element method / Stabilized method / Incompressible flows / Primitive equations of the Ocean
© EDP Sciences, SMAI, 2015
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