This paper presents an extension to stabilized methods of the standard technique for the numerical analysis of mixed methods. We prove that the stability of stabilized methods follows from an underlying discrete inf-sup condition, plus a uniform separation property between bubble and velocity finite element spaces. We apply the technique introduced to prove the stability of stabilized spectral element methods so as stabilized solution of the primitive equations of the ocean.
Mots-clés : Oseen equations, finite elements, mixed methods, stabilized methods, discrete inf-sup condition, spectral methods, primitive equations
@article{M2AN_2001__35_1_57_0,
author = {Rebollo, Tom\'as Chac\'on},
title = {An analysis technique for stabilized finite element solution of incompressible flows},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {57--89},
publisher = {EDP-Sciences},
volume = {35},
number = {1},
year = {2001},
mrnumber = {1811981},
zbl = {0990.76039},
language = {en},
url = {http://www.numdam.org/item/M2AN_2001__35_1_57_0/}
}
TY - JOUR AU - Rebollo, Tomás Chacón TI - An analysis technique for stabilized finite element solution of incompressible flows JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 57 EP - 89 VL - 35 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_2001__35_1_57_0/ LA - en ID - M2AN_2001__35_1_57_0 ER -
%0 Journal Article %A Rebollo, Tomás Chacón %T An analysis technique for stabilized finite element solution of incompressible flows %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 57-89 %V 35 %N 1 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_2001__35_1_57_0/ %G en %F M2AN_2001__35_1_57_0
Rebollo, Tomás Chacón. An analysis technique for stabilized finite element solution of incompressible flows. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 1, pp. 57-89. http://www.numdam.org/item/M2AN_2001__35_1_57_0/
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