A New Numerical Method for Solving the Stokes Problem Using Quadratic Programming
M. Baymani, A. Kerayechian
DOI: 10.4236/iim.2012.23023   PDF    HTML     4,421 Downloads   8,134 Views   Citations


In this paper we present a new method for solving the Stokes problem which is a constrained optimization method. The new method is simpler and requires less computation than the existing methods. In this method we transform the Stokes problem into a quadratic programming problem and by solving it, the velocity and the pressure are obtained.

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Baymani, M. and Kerayechian, A. (2010) A New Numerical Method for Solving the Stokes Problem Using Quadratic Programming. Intelligent Information Management, 2, 199-203. doi: 10.4236/iim.2012.23023.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] F. Brezzi and M. Fortin, “Mixed and hybrid finite element methods,” Springer-Verlag, New York, 1991.
[2] H. Elman, D. Silvester, and A. Wathen, “Finite elements and fast iterative solvers with applications in incompressible fluid dynamics,” Oxford University Press, Oxford 2005.
[3] V. Girault, and P. Raviart, “Finite element methods for Navier–Stokes equations,” Springer-Verlag, Berlin, 1986.
[4] T. Barth, P. Bochev, M. Gunzburger, and J. Shahid, “A taxomony of consistently stabilized finite element methods for stokes problem,” SIAM Journal on Scientific Computing, Vol. 25, pp. 1585–1607, 2004.
[5] L. P. Franca, T. J. R. Hughes, and R. Stenberg, “Stabilised finite element methods,” in: Incompressible Computational Fluid Dynamics Trends and Advances, Cambridge University, pp. 87–107, 1993.
[6] N. Kechkar and D. Silvester, “Analysis of locally stabilized mixed finite element methods for Stokes problem,” Mathematics of Computation, Vol. 58, pp. 1–10, 1992.
[7] R. Araya, G. R. Barrenechea, and F. Valentin, “Stabilized finite element methods based on multiscale enrichment for the Stokes problem,” SIAM journal on Numerical Analysis, Vol. 44, No. 1, pp. 322–348, 2006.
[8] G. R. Barrenechea and F. Valentin, “Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem I,” CR Academic Science, Vol. 341, pp. 635–640, 2005.
[9] E. Burman, M. Fernandez, and P. Hansbo, “Continuous interior penalty finite element method for Oseen’s equations,” SIAM Journal on Numerical Analysis, Vol. 44, No. 6, pp. 1248–1274, 2006.
[10] E. Burman and P. Hansbo, “Edge stabilization for the generalized Stokes problem: A continuous interior penalty method,” Computer Methods on Applied Mechanics and Engneering. Vol. 195, pp. 2393–2410, 2006.
[11] K. Nafa, and A. J. Wathen, “Local projection stabilized Galerkin approximations for the generalized Stokes problem,” Computer Methods on Applied Mechanics and Engneering, Vol. 198, pp. 877–883, 2009.
[12] B. Borre and N. Lukkassen, “Application of homogenization theory related to Stokes flow in porous media,” Applications of Mathematics, Vol. 44, No. 4, pp. 309–319, 1999.
[13] A. Quarteroni and A. Valli, “Numerical approximation of partial differential equations,” ISBN 3–540–57111–6, Springer-Verlag, Berlin Heidelberg, New York, 1997.
[14] S. Effati and M. Baymani, “A new nonlinear neural network for solving quadratic programming problems,” Applied Mathematics and Computational, Vol. 165, pp. 719–729, 2005.
[15] C. C. Tsai and S. Y. Yang, “On the velocity-vorticity- pressure least–squares finite element method for the stationary incompressible Oseen problem,” Journal of Com- putational and Applied Mathematics, Vol. 182, pp. 211–232, 2005.

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