Stability of a finite element method for 3D exterior stationary Navier-Stokes flows

Paul Deuring

Applications of Mathematics (2007)

  • Volume: 52, Issue: 1, page 59-94
  • ISSN: 0862-7940

Abstract

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We consider numerical approximations of stationary incompressible Navier-Stokes flows in 3D exterior domains, with nonzero velocity at infinity. It is shown that a P1-P1 stabilized finite element method proposed by C. Rebollo: A term by term stabilization algorithm for finite element solution of incompressible flow problems, Numer. Math. 79 (1998), 283–319, is stable when applied to a Navier-Stokes flow in a truncated exterior domain with a pointwise boundary condition on the artificial boundary.

How to cite

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Deuring, Paul. "Stability of a finite element method for 3D exterior stationary Navier-Stokes flows." Applications of Mathematics 52.1 (2007): 59-94. <http://eudml.org/doc/33276>.

@article{Deuring2007,
abstract = {We consider numerical approximations of stationary incompressible Navier-Stokes flows in 3D exterior domains, with nonzero velocity at infinity. It is shown that a P1-P1 stabilized finite element method proposed by C. Rebollo: A term by term stabilization algorithm for finite element solution of incompressible flow problems, Numer. Math. 79 (1998), 283–319, is stable when applied to a Navier-Stokes flow in a truncated exterior domain with a pointwise boundary condition on the artificial boundary.},
author = {Deuring, Paul},
journal = {Applications of Mathematics},
keywords = {stationary incompressible Navier-Stokes flows; exterior domains; stabilized finite element methods; stability estimates; stationary incompressible Navier-Stokes flows; exterior domains; stabilized finite element methods; stability estimates},
language = {eng},
number = {1},
pages = {59-94},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability of a finite element method for 3D exterior stationary Navier-Stokes flows},
url = {http://eudml.org/doc/33276},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Deuring, Paul
TI - Stability of a finite element method for 3D exterior stationary Navier-Stokes flows
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 1
SP - 59
EP - 94
AB - We consider numerical approximations of stationary incompressible Navier-Stokes flows in 3D exterior domains, with nonzero velocity at infinity. It is shown that a P1-P1 stabilized finite element method proposed by C. Rebollo: A term by term stabilization algorithm for finite element solution of incompressible flow problems, Numer. Math. 79 (1998), 283–319, is stable when applied to a Navier-Stokes flow in a truncated exterior domain with a pointwise boundary condition on the artificial boundary.
LA - eng
KW - stationary incompressible Navier-Stokes flows; exterior domains; stabilized finite element methods; stability estimates; stationary incompressible Navier-Stokes flows; exterior domains; stabilized finite element methods; stability estimates
UR - http://eudml.org/doc/33276
ER -

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