Geodesic
A reduced discrete inf-sup condition in L p for incompressible flows and application
Rebollo, Tomás Chacón1  ; Girault, Vivette2  ; Mármol, Macarena Gómez3  ; Muñoz, Isabel Sánchez4
1 Departamento de Ecuaciones Diferenciales y Análisis Numérico and Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Apdo. de correos 1160, Universidad de Sevilla, 41080 Sevilla, Spain
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
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 4, pp. 1219-1238

Voir la notice de l'article provenant de la source Numdam

In this work, we introduce a discrete specific inf-sup condition to estimate the L p 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 L p 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.

DOI : 10.1051/m2an/2015008
Classification : 35Q35, 65N12, 76D05
Keywords: Inf-sup condition, Finite element method, Stabilized method, Incompressible flows, Primitive equations of the Ocean

Rebollo, Tomás Chacón 1 ; Girault, Vivette 2 ; Mármol, Macarena Gómez 3 ; Muñoz, Isabel Sánchez 4

1 Departamento de Ecuaciones Diferenciales y Análisis Numérico and Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Apdo. de correos 1160, Universidad de Sevilla, 41080 Sevilla, Spain
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 
@article{M2AN_2015__49_4_1219_0,
     author = {Rebollo, Tom\'as Chac\'on and Girault, Vivette and M\'armol, Macarena G\'omez and Mu\~noz, Isabel S\'anchez},
     title = {A reduced discrete inf-sup condition in $L^{p}$ for incompressible flows and application},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1219--1238},
     publisher = {EDP-Sciences},
     volume = {49},
     number = {4},
     year = {2015},
     doi = {10.1051/m2an/2015008},
     mrnumber = {3371909},
     zbl = {1321.35154},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015008/}
}
TY  - JOUR
AU  - Rebollo, Tomás Chacón
AU  - Girault, Vivette
AU  - Mármol, Macarena Gómez
AU  - Muñoz, Isabel Sánchez
TI  - A reduced discrete inf-sup condition in $L^{p}$ for incompressible flows and application
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2015
SP  - 1219
EP  - 1238
VL  - 49
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015008/
DO  - 10.1051/m2an/2015008
LA  - en
ID  - M2AN_2015__49_4_1219_0
ER  - 
%0 Journal Article
%A Rebollo, Tomás Chacón
%A Girault, Vivette
%A Mármol, Macarena Gómez
%A Muñoz, Isabel Sánchez
%T A reduced discrete inf-sup condition in $L^{p}$ for incompressible flows and application
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2015
%P 1219-1238
%V 49
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015008/
%R 10.1051/m2an/2015008
%G en
%F M2AN_2015__49_4_1219_0
Rebollo, Tomás Chacón; Girault, Vivette; Mármol, Macarena Gómez; Muñoz, Isabel Sánchez. A reduced discrete inf-sup condition in $L^{p}$ for incompressible flows and application. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 4, pp. 1219-1238. doi: 10.1051/m2an/2015008

Cité par Sources :