Suitable initial conditions

Journal of Computational Physics

Volumn 218, Issue 2, 2006, Pages 443-450

  Temam, Roger ^a,b  

^a INDIANA UNIVERSITY   (United States)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Compatibility conditions; Initial conditions; Initial value problems; Navier Stokes equations

Indexed keywords

INITIAL VALUE PROBLEMS;

COMPATIBILITY CONDITIONS; COMPUTATIONAL PROBLEM; INITIAL CONDITIONS; INITIAL-VALUE PROBLEM; NAVIER-STOKES EQUATION;

NAVIER STOKES EQUATIONS;

EID: 33748916027     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.03.033     Document Type: Article

References (15)

1. Boyd J.P., and Flyer N. Compatibility conditions for time-dependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods (English. English summary). Comput. Methods Appl. Mech. Eng. 175 3-4 (1999) 281-309
2. Cannon C., and Rozier J. The one-dimensional heat equation. With a foreword by Felix E. Browder. Encyclopedia of Mathematics and its Applications vol. 23 (1984), Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA xxv+483 pp
3. Gallavotti G. Foundations of fluid dynamics (Translated from the Italian). Texts and Monographs in Physics (2002), Springer, Berlin xviii+513 pp
4. Gresho P.M., and Sani R.L. On pressure boundary-conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 7 10 (1987) 1111-1145
5. Gresho P.M. Incompressible fluid-dynamics - some fundamental formulation issues. Annu. Rev. Fluid Mech. 23 (1991) 413-453
6. Engelman M.S., Sani R.L., and Gresho P.M. The implementation of normal and/or tangential boundary conditions in finite element codes for incompressible fluid flow. Int. J. Numer. Methods Fluids 2 3 (1982) 225-238 76-08
7. Flyer N., and Fornberg B. Accurate numerical resolution of transients in initial-boundary value problems for the heat equation. J. Comput. Phys. 184 2 (2003) 526-539
8. Flyer N., and Swarztrauber P.N. The convergence of spectral and finite difference methods for initial-boundary value problems. SIAM J. Sci. Comput. 23 5 (2002) 1731-1751
9. Heywood J.G. Auxiliary flux and pressure conditions for Navier-Stokes problems. Approximation methods for Navier-Stokes problems (Proc. Sympos., Univ. Paderborn, Paderborn, 1979). Lecture Notes in Math. vol. 771 (1980), Springer, Berlin/New York 223-234
10. Heywood J.G., and Rannacher R. 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 2 (1982) 275-311
11. Kreiss H.O., and Lorenz J. Initial-boundary value problems and the Navier-Stokes equations. Classics in Applied Mathematics vol. 47 (2004), Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (Reprint of the 1989 edition)
12. Lions J.-L., and Magenes E. Non-homogeneous boundary value problems and applications. Vol. I. Translated from the French by P. Kenneth. Die Grundlehren der mathematischen Wissenschaften. Band vol. 181 (1972), Springer, New York/Heidelberg xvi+357 pp
13. Rauch J.B., and Massey III F.J. Differentiability of solutions to hyperbolic initial-boundary value problems. Trans. Am. Math. Soc. 189 (1974) 303-318
14. Temam R. Behaviour at time t = 0 of the solutions of semi-linear evolution equations. J. Differ. Equ. 17 (1982) 73-92
15. Temam R. Navier-Stokes Equations (1978), North-Holland, Amsterdam (Reedition in the AMS-Chelsea Series, AMS, Providence, 2001)