Stabilized finite-element method for the stationary Navier-Stokes equations

Journal of Engineering Mathematics

Volumn 51, Issue 4, 2005, Pages 367-380

  He, Yinnian ^a   Wang, Aiwen ^b   Mei, Liquan ^c  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b BEIJING INSTITUTE OF MACHINERY   (China)

^c XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Error estimation; Navier Stokes equations; Stabilized finite element

Indexed keywords

ERROR ANALYSIS; NAVIER STOKES EQUATIONS; PARAMETER ESTIMATION;

MACROELEMENT CONDITIONS; OPTIMAL ERROR ESTIMATES; TRAINGULAR ELEMENTS;

FINITE ELEMENT METHOD;

NAVIER-STOKES EQUATIONS;

EID: 20344375713     PISSN: 00220833     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10665-004-3718-5     Document Type: Article

References (20)

1. V. Girault and P.A. Raviart 1981 Finite Element Method for Navier-Stokes Equations: Theory and Algorithms Springer-Verlag Berlin Heidelberg 202 pp.
2. J. Boland and R.A. Nicolaides 1983 Stability of finite elements under divergence constraints SIAM J. Numer. Anal. 20 722-731 10.1137/0720048
3. R. Stenberg 1984 Analysis of mixed finite elements for the Stokes problem: A unified approach Math. Comp. 42 9-23
4. N. Kechkar and D. Silvester 1992 Analysis of locally stabilized mixed finite element methods for the Stokes problem Math. Comp. 58 1-10
5. D.J. Silvester and N. Kechkar 1990 Stabilised bilinear-constant velocity-pressure finite elements for the conjugate gradient solution of the Stokes problem. Comp Methods Appl. Mech. Engng 79 71-86 10.1016/ 0045-7825(90)90095-4
6. D. Kay and D. Silvester 2000 A posteriori error estimation for stabilized mixed approximations of the Stokes equations SIAM J. Sci. Comp. 21 1321-1337 10.1137/S1064827598333715
7. S. Norburn and D. Silvester 1998 Stabilised vs. stable mixed methods for incompressible flow Comput. Methods Appl. Mech. Engng. 166 1-10 10.1016/ S0045-7825(98)00078-4
8. D. Silvester and A. Wathen 1994 Fast interative solution of stabilised Stokes systems, Part II: Using general block preconditioners SIAM J. Numer. Anal. 31 1352-1367 10.1137/0731070
9. D. Braess 1997 Finite Elements, Theory, Fast Solvers and Applications in Solid Mechnics Cambridge University Press Cambridge 323 pp.
10. J. Pitkäranta and T. Saarinen 1985 A multigrid version of a simple finite element method for the Stokes problem Math. Comput. 45 1-14
11. J.G. Heywood and R. Rannacher 1982 Finite element approximation of the nonstationary Navier-Stokes problem, I: Regularity of solutions and second-order error estimates for spatial discretization SIAM J. Numer. Anal. 19 275-311 10.1137/0719018
12. R.B. Kellogg and J.E. Osborn 1976 A regularity result for the Stokes problem in a convex polygon J. Funct. Anal. 21 397-431 10.1016/ 0022-1236(76)90035-5
13. A. AitOu Ammi and M. Marion 1994 Nonlinear Galerkin methods and mixed finite elements: Two-grid algorithms for the Navier-Stokes equations Numer. Math. 68 189-213 10.1007/s002110050056
14. R. Temam 1984 Navier-Stokes Equations, Theory and Numerical Analysis North-Holland Amsterdam 526 pp.
15. P.G. Ciarlet 1978 The Finite Element Method for Elliptic Problems North-Holland Amsterdam 519 pp.
16. Sani R.L., Gresho P.M., Lee R.L. and D.F. Griffiths, The cause and cure(?) of the spuious pressures generated by certain finite element method solutions of the incompressible Navier-Stokes equations. Parts 1 and 2. Int. J. Numer. Methods Fluids 1 (1981) 17-43; 171-206
17. T.J.R. Hughes and L.P. Franca 1987 A new finite element formulation for CFD: VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/ pressure spaces. Comput. Methods Appl. Mech. Engng. 65 85-97
18. W. Layton and L. Tobiska 1998 A two-level method with backtraking for the Navier-Stokes equations SIAM J. Numer. Anal. 35 2035-2054 10.1137/ S003614299630230X
19. A.J. Baker 1983 Finite Element Computational Fluid Mechanics Hemisphere Pub. Corp Washington 510 pp.
20. T.J.R. Hughes W.K. Liu and A. Brooks 1979 Review of finite element analysis of incompressible viscous flow by the penalty function formulations J. Comp Phys. 30 1-60 10.1016/0021-9991(79)90086-X