A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations

Robert Renka

Open Mathematics (2013)

  • Volume: 11, Issue: 4, page 630-641
  • ISSN: 2391-5455

Abstract

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The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.

How to cite

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Robert Renka. "A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations." Open Mathematics 11.4 (2013): 630-641. <http://eudml.org/doc/269068>.

@article{RobertRenka2013,
abstract = {The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.},
author = {Robert Renka},
journal = {Open Mathematics},
keywords = {Finite element method; Least squares; Navier-Stokes; Sobolev gradient; Trust region; finite element method; least squares; trust region},
language = {eng},
number = {4},
pages = {630-641},
title = {A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations},
url = {http://eudml.org/doc/269068},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Robert Renka
TI - A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations
JO - Open Mathematics
PY - 2013
VL - 11
IS - 4
SP - 630
EP - 641
AB - The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.
LA - eng
KW - Finite element method; Least squares; Navier-Stokes; Sobolev gradient; Trust region; finite element method; least squares; trust region
UR - http://eudml.org/doc/269068
ER -

References

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