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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0201-4,
author = {Robert Renka},
title = {A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {630-641},
zbl = {1260.76016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0201-4}
}
Robert Renka. A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations. Open Mathematics, Tome 11 (2013) pp. 630-641. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0201-4/
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