Abstract
We consider two-level finite element discretization methods for the stream function formulation of the Navier-Stokes equations. The two-level method consists of solving a small nonlinear system on the coarse mesh, then solving a linear system on the fine mesh. It is shown in [8] that the errors between the coarse and fine meshes are related superlinearly. This paper presents an algorithm for pressure recovery and a general analysis of convergence for the algorithm. The numerical example for the 2D driven cavity fluid is considered. Streamfunction contours are displayed showing the main features of the flow.
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References
J. Akin. finite element for analysis and design. Academic Press, San Diego, 1994.
I. Babuska and A. K. Aziz. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. Academic Press, New York, 1972.
R. Barrett, M. Berry T. Chan J. Demmel J. Donator J. Doncarra V. Eijkhout R. Pozo C. Romine and H. Van dev Vorst, Templates: for the solution of linear systems: building blocks for iterative methods. e-mail: templates@cs.utk.edu.
M. Cayco. Finite Element Methods for the Stream Function Formulation of the Navier-Stokes Equations. PhD thesis, CMU, Pittsburgh, PA., 1985.
M. Cayco and R. A. Nicolaides. Analysis of nonconforming stream function and pressure finite element spaces of the Navier-Stokes equations. Gomp. and Math. Appl., (8): 745–760, 1989.
M. Cayco and R. A. Nicolaides. Finite element technique for optimal pressure recovery from stream function formulation of viscous flows. Math. Gomp., (56): 371–377, 1986.
Ph. G. Ciarlet, the finite element method for elliptic problems, North Holland, Amsterdam, 1978
F. Fairag. Two-level finite element method for the stream function formulation of the Navier-Stokes equations. Computers Math. Applic., 36(2): 117–127, 1998.
K. N. Ghia U. Ghia and C. T. Shin. High Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comput. Phys., 48: 387–411, 1982.
V. Girault and P. A. Raviart. Finite Element Approximation of the Navier-Stokes Equations, volume 749. Springer, Berlin, 1979.
W. Layton. A two-level discretization method for the Navier-Stokes equations. Computers Math. Applic., 26:33–38, 1993.
W. Layton and W. Lenferink. Two-level Picard-defect corrections for the Navier-Stokes equations at high Reynolds number. Applied Math. and Computing, 1995.
W. Layton and W. Lenferink, A multilevel mesh independence principle for the Navier-Stokes equations, SIAM J. N. A. (1996)
J. Xu. A novel two-grid method for semilinear elliptic equations. SIAM J. Sci. Comput. 15(1): 231–237, 1994.
J. Xu, Some Two-Grid Finite Element Methods, chapter 157, pages 79–87. Number 157 in In Domain Decomposition Methods in Science and Engineering. Amer. Math. Soc., Providence, RI, 1994.
J. Xu. Some two-grid finite element methods. Technical report, P. S. U., 1992.
X. Ye. Two-level discretizations of the stream function form of the Navier-Stokes equations. University of Pittsburgh.
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© 2002 Springer-Verlag Berlin Heidelberg
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Fairag, F. (2002). Two Level Finite Element Technique for Pressure Recovery from Stream Function Formulation of the Navier-Stokes Equations. In: Barth, T.J., Chan, T., Haimes, R. (eds) Multiscale and Multiresolution Methods. Lecture Notes in Computational Science and Engineering, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56205-1_7
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DOI: https://doi.org/10.1007/978-3-642-56205-1_7
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