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2013 | 11 | 4 | 630-641
Tytuł artykułu

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

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Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
4
Strony
630-641
Opis fizyczny
Daty
wydano
2013-04-01
online
2013-01-29
Twórcy
autor
Bibliografia
  • [1] Agmon S., Douglis A., Nirenberg L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math., 1964, 17(1), 35–92 http://dx.doi.org/10.1002/cpa.3160170104
  • [2] Bochev P.B., Analysis of least-squares finite element methods for the Navier-Stokes equations, SIAM J. Numer. Anal., 1997, 34(5), 1817–1844 http://dx.doi.org/10.1137/S0036142994276001
  • [3] Bochev P.B., Gunzburger M.D., Analysis of least squares finite element methods for the Stokes equations, Math. Comp., 1994, 63(208), 479–506 http://dx.doi.org/10.1090/S0025-5718-1994-1257573-4
  • [4] Bochev P.B., Gunzburger M.D., Least-Squares Finite Element Methods, Appl. Math. Sci., 166, Springer, New York, 2009
  • [5] Bramble J.H., Lazarov R.D., Pasciak J.E., A least-squares approach based on a discrete minus one inner product for first order systems, Math. Comp., 1997, 66(219), 935–955 http://dx.doi.org/10.1090/S0025-5718-97-00848-X
  • [6] Deang J.M., Gunzburger M.D., Issues related to least-squares finite element methods for the Stokes equations, SIAM J. Sci. Comput., 1998, 20(3), 878–906 http://dx.doi.org/10.1137/S1064827595294526
  • [7] Ghia U., Ghia K.N., Shin C.T., High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 1982, 48(3), 387–411 http://dx.doi.org/10.1016/0021-9991(82)90058-4
  • [8] Jiang B.N., A least-squares finite element method for incompressible Navier-Stokes problems, Internat. J. Numer. Methods Fluids, 1992, 14(7), 843–859 http://dx.doi.org/10.1002/fld.1650140706
  • [9] Jiang B., The Least-Squares Finite Element Method, Sci. Comput., Springer, Berlin, 1998 http://dx.doi.org/10.1007/978-3-662-03740-9
  • [10] Jiang B.-N., Lin T.L., Povinelli L.A., Large-scale computation of incompressible viscous flow by least-squares finite element method, Comput. Methods Appl. Mech. Engrg., 1994, 114(3–4), 213–231 http://dx.doi.org/10.1016/0045-7825(94)90172-4
  • [11] Kazemi P., Renka R.J., A Levenberg-Marquardt method based on Sobolev gradients, Nonlinear Anal., 2012, 75(16), 6170–6179 http://dx.doi.org/10.1016/j.na.2012.06.022
  • [12] Layton W., Introduction to the Numerical Analysis of Incompressible Viscous Flows, Comput. Sci. Eng., 6, Society for Industrial and Applied Mathematics, Philadelphia, 2008 http://dx.doi.org/10.1137/1.9780898718904
  • [13] Neuberger J.W., Sobolev Gradients and Differential Equations, 2nd ed., Lecture Notes in Math., 1670, Springer, Berlin, 2010 http://dx.doi.org/10.1007/978-3-642-04041-2
  • [14] Nocedal J., Wright S.J., Numerical Optimization, Springer Ser. Oper. Res., Springer, New York, 1999 http://dx.doi.org/10.1007/b98874
  • [15] Renka R.J., Nonlinear least squares and Sobolev gradients, Appl. Numer. Math., 2013, 65, 91–104 http://dx.doi.org/10.1016/j.apnum.2012.12.002
  • [16] Strang G., Fix G., An Analysis of the Finite Element Method, 2nd ed., Wellesley-Cambridge Press, Wellesley, 2008
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0201-4
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