A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 6, p. 903-924

It is well known that the classical local projection method as well as residual-based stabilization techniques, as for instance streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic meshes. Here we extend the local projection stabilization for the Navier-Stokes system to anisotropic quadrilateral meshes in two spatial dimensions. We describe the new method and prove an a priori error estimate. This method leads on anisotropic meshes to qualitatively better convergence behavior than other isotropic stabilization methods. The capability of the method is illustrated by means of two numerical test problems.

DOI : https://doi.org/10.1051/m2an:2008032
Classification:  35Q30,  65N30,  76D05
Keywords: incompressible flow, Navier-Stokes equations, stabilized finite elements, anisotropic meshes
@article{M2AN_2008__42_6_903_0,
     author = {Braack, Malte},
     title = {A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {6},
     year = {2008},
     pages = {903-924},
     doi = {10.1051/m2an:2008032},
     zbl = {1149.76026},
     mrnumber = {2473313},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2008__42_6_903_0}
}
Braack, Malte. A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 6, pp. 903-924. doi : 10.1051/m2an:2008032. http://www.numdam.org/item/M2AN_2008__42_6_903_0/

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