A Posteriori Error Estimators for a Two-Level Finite Element Method for the Navier-Stokes Equations

Numerical Methods for Partial Differential Equations

Volumn 12, Issue 3, 1996, Pages 333-346

  Ervin, V ^a,b   Layton, W ^a   Maubach, J ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

^b CLEMSON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000712897     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199605)12:3<333::AID-NUM4>3.0.CO;2-P     Document Type: Article

References (38)

1. J. Xu, "Finite element error analysis for linear and nonlinear elliptic equations and two-grid discretization techniques," SIAM J. Numer. Anal., to appear.
2. J. Xu, "Some two-grid finite element methods," Tech. Report P.S.U. (1992).
3. R. Rannacher, "On the convergence of the Newton-Raphson method for strongly nonlinear finite element equations," in Nonlinear Computational Mechanics, P. Wriggers and W. Wagner, Eds., Springer-Verlag, Berlin, 1991.
4. G. Vainikko, "Galerkin's perturbation method and the general theory of approximation for nonlinear equations," USSR Comp. Math. Phys. 7, 1 (1967).
5. K. Witsch, "Projektive Newton-Verfahren und Anwendungen auf nichtlineare Randwertaufgaben," Numer. Math. 31, 209 (1978).
6. W. Layton, "A two level discretization method for the Navier-Stokes equations," Comput. Math. Appl. 26, 33 (1993).
7. W. Layton and W. Lenferink, "Two-level Picard-defect correction for the Navier-Stokes equations," Applied Math. Comp., to appear.
8. W. Layton and W. Lenferink, "A multilevel mesh independence principle for the Navier-Stokes equations," SIAM J.N.A., to appear.
9. W. Lenferink, "An accurate solution procedure for fluid flow with natural convection," Num. Funct. Anal. Appls., to appear.
10. W. Layton, W. Lenferink, and J. Peterson, "A two-level Newton, finite element algorithm for approximating electrically conducting, incompressible fluid flows," Computers Math. Appls. 28, 21 (1994).
11. W. Lenferink and J. Maubach, "Two level global parameter-space, state-space finite element methods for branches of nonsingular solutions," Tech. Report (1994).
12. W. Layton, "Solution algorithms for incompressible viscous flows at high Reynolds number," Vestnik Mosk. Gos. Univ., Series 15, No. 4 (1994).
13. W. Layton, "A nonlinear subgridscale model for incompressible, viscous flow problems," SIAM J.S.S.C., to appear.
14. I. Babuska and W. C. Rheinboldt, "Error estimates for adaptive finite element computations," SIAM J.N.A. 15, 736 (1978).
15. M. Ainsworth and J. T. Oden, "A unified approach to a posteriori error estimation using element residual methods," Num. Math. 65, 23 (1993).
16. I. Babuska and A. Miller, "A posteriori error estimates and adaptive techniques for the finite element method," U. of Maryland Tech. Note BN-968 (1981).
17. R. E. Bank and Weiser, "Some a posteriori error estimators for elliptic partial differential equations," Math. Comp. 44, 283 (1985).
18. R. E. Bank and B. D. Welfert, "A posteriori error estimates for the Stokes equations: a comparison," Comp. Meth. Appl. Mech. Eng. 87, 323 (1990).
19. K. Eriksson and C. Johnson, "Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems," Math. Comp. 60, 167 (1993).
20. V. Ervin, W. Layton, and J. Maubach, "Residual estimators for convection dominated, convection diffusion equations," I.C.M.A. Tech. Report, Univ. of Pittsburgh, 1995.
21. V. Ervin, W. Layton, and J. Maubach, "A posteriori error control for an abstract defect correction method," I.C.M.A. Tech. Report, Univ. of Pittsburgh, 1995.
22. P. J. Rabier, "A posteriori error estimation "new" approach," I.C.M.A. Report 94-188, Univ. of Pittsburgh, 1994.
23. T. Strouboulis and J. T. Oden, "A posteriori error estimation of finite element approximations in fluid mechanics," Comp. Meth. Appl. Mech. Eng. 78, 201 (1990).
24. R. Verfürth, "A posteriori error estimators and adaptive mesh refinement techniques for the Navier-Stokes equations," in Incompressible CFD-Trends and Advances, M. D. Gunzburger and R. A. Nicolaides, Eds., Cambridge Univ. Press, 1992.
25. R. Verfürth, "A review of a posteriori error estimation and adaptive mesh refinement techniques," Universität Zurich (1993).
26. V. Girault and P.-A. Raviart, "Finite element methods for the Navier-Stokes equations," in Theory and Algorithms, Springer-Verlag, Berlin, 1986.
27. M. Gunzburger, "Finite element methods for viscous incompressible flow," in A Guide to Theory, Practice and Algorithms, Academic Press, Boston, 1989.
28. Ph. Clément, "Approximation by finite element functions using local regularization," RAIRO Anal. Numer. 2, 77 (1975).
29. C. Heusser, "Conjugate gradient-type algorithms for a finite element discretization of the Stokes equations," J. Comp. Appl. Math. 39, 23 (1992).
30. A. H. Stroud, Approximate Calculation of Multiple Integrals, Prentice-Hall, New York, 1971.
31. R. S. Dembo, S. C. Eisenstat, and T. Steihaug, "Inexact Newton methods," SIAM J.N.A. 19, 400 (1982).
32. P. Sonneveld, "CGS, a fast Lanczos-type solver for non-symmetric linear systems," SIAM J. Sci. Comput. 10, 36 (1989).
33. Y. Saad and M. H. Schultz, GMRES: "A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM J. Sci. Comput. 7, 856 (1986).
34. O. Axelsson, "A generalized conjugate gradient, least square method," Numerische Mathematik 51, 209 (1987).
35. M. J. Todd, "The computation of fixed points and applications," in Lecture Notes in Economics and Mathematical Systems 124, Springer-Verlag, Berlin, 1976.
36. J. Maubach, "Local bisection refinement for n-simplicial grids generated by reflections," SIAM J. Sci. Comput. 16 210 (1995).
37. G. C. Carey and J. T. Oden, Finite Elements, Vol VI: Fluid Mechanics, Prentice Hall, Englewood Cliffs, N. J., 1986.
38. W. C. Rheinboldt and J. L. Liu, "A posteriori error estimates for parametrized nonlinear equations," I.C.M.A. Report 90-151, Univ. of Pittsburgh, 1990.