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MULTIGRID METHODS FOR THE generalized stokes equations BASED ON MIXED FINITE ELEMENT METHODS

Journal of Computational Mathematics 2002年第2期20卷 129-152页

作者： Qing-ping Deng Xiao-ping Feng Department of Mathematics The University of Tennessee 美国 Knoxville TN 37996

Examines multigrid methods for the generalized stationary stokes equations which are discretized by various mixed finite element methods. Information on a multigrid algorithm; preliminaries of convergence; Application... 详细信息

关键词： generalized stokes equations Mixed methods Multigrid methods.

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ERROR ANALYSIS OF A STABILIZED FINITE ELEMENT METHOD FOR THE generalized stokes PROBLEM

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Journal of Computational Mathematics 2020年第2期38卷 254-290页

作者： Huoyuan Duan Roger C.E.Tan School of Mathematics and Statistics Wuhan UniversityWuhan 430072China Department of Mathematics National University of SingaporeSingapore

This paper is devoted to the establishment of sharper a priori stability and error estimates of a stabilized finite element method proposed by Barrenechea and Valentin for solving the generalized stokes problem,which involves a viscosity v and a reaction consta nt *** the establishmen t of sharper st ability estimates and the help of ad hoc finite element projections,we can explicitly establish the dependence of error bounds of velocity and pressure on the viscosity z/,the reaction constant cr,and the mesh size *** analysis reveals that the viscosity y and the reaction constant a respectively act in the numerator position and the denominator position in the error estimates of velocity and pressure in standard norms without any ***,the stabilization method is indeed suitable for the generalized stokes problem with a small viscosity u and a large reaction constant *** sharper error estimates agree very well with the numerical results.

关键词： generalized stokes equations Stabilized finite element method Error estimates.

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Improved Local Projection for the generalized stokes Problem

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Advances in Applied Mathematics and Mechanics 2009年第6期1卷 862-873页

作者： Kamel Nafa Department of Mathematics and Statistics Sultan Qaboos UniversityCollege of ScienceP.O.Box 36Al-Khoudh 123MuscatOMAN

We analyze pressure stabilized finite element methods for the solution of the generalized stokes problem and investigate their stability and convergence *** important feature of the methods is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of *** the stability of the method has been established,for the homogeneous stokes equations,the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection *** makes it much simpler and more *** resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations.

关键词： generalized stokes equations stabilized finite elements local projection convergence error estimates

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The Lid-Driven Square Cavity Flow: From Stationary to Time Periodic and Chaotic

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Communications in Computational Physics 2007年第5期2卷 900-932页

作者： Salvador Garcia Departamento de Ciencias Matem´aticas y F´ısicas Universidad Cat´olica de TemucoCasilla 15-D TemucoChile

Ranging from Re=100 to Re=20,000,several computational experiments are conducted,Re being the Reynolds *** primary vortex stays put,and the longterm dynamic behavior of the small vortices determines the nature of the *** low Reynolds numbers,the solution is stationary;for moderate Reynolds numbers,it is time *** high Reynolds numbers,the solution is neither stationary nor time periodic:the solution becomes *** the small vortices,the merging and the splitting,the appearance and the disappearance,and,sometime,the dragging away from one corner to another and the impeding of the merging—these mark the route to *** high Reynolds numbers,over weak fundamental frequencies appears a very low frequency dominating the spectra—this very low frequency being weaker than clear-cut fundamental frequencies seems an indication that the global attractor has been *** global attractor seems reached for Reynolds numbers up to Re=15,*** is the lid-driven square cavity flow;the motivations for studying this flow are recalled in the Introduction.

关键词： Finite differences staggered marker-and-cell(MAC)mesh incremental unknowns generalized stokes equations incompressible Navier-stokes equations chaos.

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