# A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 42, Issue: 6, page 903-924
- ISSN: 0764-583X

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topBraack, Malte. "A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes." ESAIM: Mathematical Modelling and Numerical Analysis 42.6 (2008): 903-924. <http://eudml.org/doc/250406>.

@article{Braack2008,

abstract = {
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.
},

author = {Braack, Malte},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Incompressible flow; Navier-Stokes equations; stabilized finite
elements; anisotropic meshes.; a priori error estimate},

language = {eng},

month = {8},

number = {6},

pages = {903-924},

publisher = {EDP Sciences},

title = {A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes},

url = {http://eudml.org/doc/250406},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Braack, Malte

TI - A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/8//

PB - EDP Sciences

VL - 42

IS - 6

SP - 903

EP - 924

AB -
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.

LA - eng

KW - Incompressible flow; Navier-Stokes equations; stabilized finite
elements; anisotropic meshes.; a priori error estimate

UR - http://eudml.org/doc/250406

ER -

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