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

Open Mathematics (2013)

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

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topRobert 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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