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

Malte Braack

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

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

Abstract

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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.

How to cite

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Braack, 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 -

References

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