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Keywords: Navier-Stokes equations, Oseen equations, characteristics method, pressure-stabilization, error estimates, stability.

Summary

In this paper stabilized Galerkin-characteristics finite element schemes for the Oseen and the Navier-Stokes equations are analyzed to be stable and convergent. The former is unconditionally stable, and the latter is conditionally stable as a result of the nonlinearity but the condition is revealed to be non-restrictive essentially in real computation. The error estimates of both of the schemes are optimal. By virtue of the property of the characteristics method the schemes are robust for high Reynolds number problems. The schemes employ an inexpensive P1/P1 element which yields a small number of degrees of freedom. Since matrices derived from the schemes are symmetric, powerful linear solvers for symmetric systems of linear equations can be used. The schemes are, therefore, efficient especially for three-dimensional problems. Numerical results from the scheme for the Navier-Stokes equations are presented to show its effectiveness.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 105 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: Paper 71 Stabilized Galerkin-Characteristics Finite Element Schemes for Flow Problems H. Notsu¹ and M. Tabata² ¹Waseda Institute for Advanced Study, Waseda University, Tokyo, Japan ²Department of Mathematics, Waseda University, Tokyo, Japan doi:10.4203/ccp.105.71 purchase the full-text of this paper Full Bibliographic Reference for this paper H. Notsu, M. Tabata, "Stabilized Galerkin-Characteristics Finite Element Schemes for Flow Problems", in , (Editors), "Proceedings of the Ninth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 71, 2014. doi:10.4203/ccp.105.71 Keywords: Navier-Stokes equations, Oseen equations, characteristics method, pressure-stabilization, error estimates, stability. Summary In this paper stabilized Galerkin-characteristics finite element schemes for the Oseen and the Navier-Stokes equations are analyzed to be stable and convergent. The former is unconditionally stable, and the latter is conditionally stable as a result of the nonlinearity but the condition is revealed to be non-restrictive essentially in real computation. The error estimates of both of the schemes are optimal. By virtue of the property of the characteristics method the schemes are robust for high Reynolds number problems. The schemes employ an inexpensive P1/P1 element which yields a small number of degrees of freedom. Since matrices derived from the schemes are symmetric, powerful linear solvers for symmetric systems of linear equations can be used. The schemes are, therefore, efficient especially for three-dimensional problems. Numerical results from the scheme for the Navier-Stokes equations are presented to show its effectiveness. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £45 +P&P)
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