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.
@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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {35},
year = {2001},
pages = {57-89},
mrnumber = {1811981},
zbl = {0990.76039},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2001__35_1_57_0}
}
Rebollo, Tomás Chacón. An analysis technique for stabilized finite element solution of incompressible flows. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001) pp. 57-89. http://gdmltest.u-ga.fr/item/M2AN_2001__35_1_57_0/
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