Abstract
In this paper, a new approach for finding the approximate solution of the Stokes problem is introduced. In this method the problem is transformed to an equivalent optimization problem. Then, by considering it as a distributed parameter control system, the theory of measure is used to approximate the velocity functions by piecewise linear functions. Then, the approximate values of pressure are obtained by a finite difference scheme.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Gachpazan, A. Kerayechian and A. V. Kamyad,A new method for solving nonlinear second order partial differential equations, The Koraen Journal of Computational and Applied Mathematics, Vol.7, No. 2, 2000.
V. Girault and P. A. Ravirat,Finite element approximation of the Navier-Stokes equations, Lecture Notes in Mathematics, Springer-Verlag,749, 1981.
D. Greenspan and V. Casulli,Numerical analysis for applied mathematics, science and engineering, Addison-Wesley, 1988.
J. E. Rubio,Control and Optimization: The Linear Treatment of nonlinear Problems, Manchester, U.K. Manchester University Press, 1986.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gachpazan, M., Kerayechian, A. A new approach for solving the Stokes problem. Korean J. Comput. & Appl. Math. 8, 151–164 (2001). https://doi.org/10.1007/BF03011629
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF03011629