A sequential regularization method for time-dependent incompressible navier-stokes equations

SIAM Journal on Numerical Analysis

Volumn 34, Issue 3, 1997, Pages 1051-1071

  Lin, Ping ^a,b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Asymptotic analysis; Energy estimates; Finite difference; Navier stokes equations; Regularization method

Indexed keywords

EID: 0012150867     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994270521     Document Type: Article

References (35)

1. C. AMIROUCHE AND V. GIRAULT, Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Math. J., 44 (1994), pp. 109-140.
2. K. ARROW, L. HURWICZ, AND H. UZAWA, Studies in Nonlinear Programming, Stanford University Press, Stanford, CA, 1968.
3. U. ASCHER AND P. LIN, Sequential regularization methods for higher index DAEs with constraint singularities: Linear index-2 case, SIAM J. Numer. Anal., 33 (1996), pp. 1921-1940.
4. U. ASCHER AND P. LIN, Sequential regularization methods for nonlinear higher index DAEs, SIAM J. Sci. Comput., 18 (1996), pp. 160-181.
5. J. BAUMGARTE, Stabilization of constraints and integrals of motion in dynamical systems, Comput. Methods Appl. Mech. Engrg., 1 (1972), pp. 1-16.
6. E. BAYO AND A. AVELLO, Singularity-free augmented Lagrangian algorithms for constrained multibody dynamics, J. Nonlinear Dynamics, 5 (1994), pp. 209-231.
7. A. BRANDT, Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, The Weizmann Institute of Science, Rehovot, Israel, 1984.
8. B. BREFORT, J. M. GHIDAGLIA, AND R. TEMAM, Attractors for the penalized Navier-Stokes equations, SIAM J. Math. Anal., 19 (1988), pp. 1-21.
9. K. BRENAN, S. CAMPBELL, AND L. PETZOLD, Numerical Solutions of Initial-Value Problems in Differential-Algebraic Equations, Elsevier, New York, 1989.
10. C. CANUTO, M.Y. HUSSAINI, A. QUARTERONI, AND T.A. ZANG, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, New York, 1987.
11. A.J. CHORIN, Numerical solution of the Navier-Stokes equations, Math. Comp., 22 (1968). pp. 745-762.
12. M. FORTIN AND R. GLOWINSKI, Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, Stud. Math. Appl., 15, North-Holland, Amsterdam, 1983.
13. V. GIRAULT AND P.A. RAVIART, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, Berlin, Heidelberg, 1986.
14. E. GRIEPENTROG AND R. MÄRZ, Differential-Algebraic Equations and their Numerical Treatment, Teubner-Texte Math., 88, Leipzig, 1986.
15. P.M. GRESHO, Some current issues relevant to the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 87 (1987), pp. 201-252.
16. E. HAIRER AND G. WANNER, Solving Ordinary Differential Equations II, Springer-Verlag, Berlin, New York, 1991.
17. M. HANKE. Regularization of Differential-Algebraic Equations Revisited, Preprint No. 92-19. Humboldt Univ., Fachbereich Mathematik, Berlin, 1992.
18. J.G. HEYWOOD, The Navier-Stokes equations: On the existence, regularity and decay of solutions, Indiana Univ. Math. J., 29 (1980), pp. 639-681.
19. J.G. HEYWOOD AND R. RANNACHER, 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 (1982), pp. 275-311.
20. C. HIRSCH, A general analysis of two-dimensional convection schemes, VKI Lecture Series 1991-02 on Computational Fluid Dynamics, Von Karman Institute, Brussels, Belgium, 1991.
21. T.Y. HOU AND B.T.R. WETTON, Convergence of a finite difference scheme for the Navier-Stokes equations using vorticity boundary conditions, SIAM J. Numer. Anal., 29 (1992), pp. 615-639.
22. L. KALACHEV AND R. O'MALLEY, JR., The regularization of linear differential-algebraic equations, SIAM J. Math. Anal., 27 (1996), pp. 258-273.
23. H.-O. KREISS AND J. LORENZ, Initial-Boundary Value Problems and the Navier-Stokes Equations, Pure and Applied Mathematics, Vol. 136, Academic Press, New York, San Diego, CA, 1989.
24. M. LEES, A priori estimates for the solutions of difference approximations to parabolic partial differential equations, Duke Math J., 27 (1960), pp. 297-311.
25. P. LIN AND D. Q. YANG, An iterative perturbation method for the pressure equation in the simulation of miscible displacement in porous media, SIAM J. Sci. Comput., to appear.
26. J. NECAS, Les methodes directes en theorie des equations elliptiques, Academia, Prague, 1967.
27. K. PARK AND J. CHIOU. Stabilization of computational procedures for constrained dynamical systems, J. Guidance Control Dynamics, 11 (1988), pp. 365-370.
28. R. RANNACHER, On Chorin's projection for the incompressible Navier-Stokes equations, in Navier-Stokes Equations: Theory and Numerical Methods. Proc. Oberwolfach Conf., 19.23.8.1991, Rautmann et al., eds., Springer-Verlag, Heidelberg, 1992.
29. R. RANNACHER, On the numerical solution of the incompressible Navier-Stokes equations, Z. Angew. Math. Mech., 73 (1993), pp. 203-216.
30. J. SHEN, On error estimates of projection methods for the Navier-Stokes equations: First-order schemes, SIAM J. Numer. Anal., 29 (1992), pp. 57-77.
31. D. SIDILKOVER AND U.M. ASCHER, A multigrid solver for the steady state Navier-Stokes equations using the pressure-Poisson formulation, Tech. Report 94-3, Dept. of Computer Science, University of British Columbia. Canada. 1994.
32. Y. SU AND P. LIN, Uniform difference scheme for a singularly perturbed linear 2nd order hyperbolic problem with zero-th order reduced equation, App. Math. Mech., 11 (1990), pp. 301-313.
33. R. TEMAM, Navier-Stokes Equations, North-Holland, Amsterdam, 1977.
34. S. TUREK, Tools for Simulating Nonstationary Incompressible Flow via Discretely Divergence-Free Finite Element Models, Universität Heidelberg, May 1992, preprint.
35. 2-Laplacians and zero boundary values on arbitrary three-dimensional domains. Indiana University Math. J., 40 (1991), pp. 1185-1192.