In this paper, we analyze a class of stabilized finite element formulations used in computation of (i) second order elliptic boundary value problems (diffusion-convection-reaction model) and (ii) the Navier-Stokes problem (incompressible flow model). These stabilization techniques prevent numerical instabilities that might be generated by dominant convection/reaction terms in (i), (ii) or by inappropriate combinations of velocity/pressure interpolation functions in (ii). Stability and convergence results on non-uniform meshes are given in the whole range from diffusion to convection/reaction dominated situations. In particular, we recover results for the streamline upwind and Galerkin/least-squares methods. Numerical results are presented for low order interpolation functions.
@article{bwmeta1.element.bwnjournal-article-bcpv29z1p85bwm,
author = {Lube, Gert},
title = {Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems},
journal = {Banach Center Publications},
volume = {29},
year = {1994},
pages = {85-104},
zbl = {0801.76046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv29z1p85bwm}
}
Lube, Gert. Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems. Banach Center Publications, Tome 29 (1994) pp. 85-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv29z1p85bwm/
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