Least-squares spectral collocation with the overlapping Schwarz method for the incompressible Navier-Stokes equations

Numerical Algorithms

Volumn 43, Issue 1, 2006, Pages 61-73

  Heinrichs, Wilhelm ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

Driven cavity flow; Least squares; Navier Stokes; Overlapping Schwarz; Spectral collocation

Indexed keywords

EID: 33751578253     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-006-9039-1     Document Type: Article

References (26)

1. Bernardi, C., Canuto, C., Maday, Y.; Generalized inf-sup condition for Chebyshev approximations to Navier-Stokes equations. C.R. Acad. Sci. Paris 303(serie I). 971-974 (1986)
2. Bernardi, C., Maday, Y.: Approximations Spectrale de Problémes aux Limites Elliptiques. Springer, Berlin Heidelberg New York (1992)
3. Botella, O.: On the solution of the Navier-Stokes equations using Chebyshev projection schemes with third-order accuracy in time. Computer Fluids 26, 107 (1997)
4. Botella, O., Peyret, R.: Benchmark spectral results on the lid-driven cavity flow. Computer Fluids 27(4), 421-433 (1998)
5. Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods in Fluid Dynamics, Springer Series in Computational Physics. Springer, Berlin Heidelberg New York (1989)
6. Deang, J.M., Gunzburger, M.D.: Issues related to least-squares finite element methods for the Stokes equations. SIAM J. Sci. Comput. 20, 878-906 (1998)
7. Deville, M.O., Fischer, P.F., Mund, E.H.: High-Order Methods for Incompressible Fluid Flow, Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, New York (2002)
8. Eisen, H., Heinrichs, W.: A new method of stabilization for singular perturbation problems with spectral methods. SIAM J. Numer. Anal. 29, 107-122 (1992)
9. Gerritsma, M.I., Phillips, T.N.: Discontinuous spectral element approximation for the velocity-pressure-stress formulation of the Stokes problem. Int. J. Numer. Methods Eng. 43, 1401-1419 (1998)
10. Gerritsma, M.I., Proot, M.J.: Analysis of a discontinuous least-squares spectral element method. J. Sci. Comput. 17, 297-306 (2002)
11. Gottlieb, D., Orszag, S.A.: Numerical Analysis of Spectral Methods: Theory and Applications. CBMS-NSF Regional Conference Series in Applied Mathematics no. 26. SIAM, Philadelphia (1977)
12. Haschke, H., Heinrichs, W.: Splitting techniques with staggered grids for the Navier-Stokes equations in the 2D case. J. Comput. Phys. 168, 131-154 (2001)
13. Heinrichs, W.: A stabilized multidomain approach for singular perturbation problems. J. Sci. Comput. 7(2), 95-125 (1992)
14. Heinrichs, W.: Splitting techniques for the pseudospectral approximation of the unsteady Stokes equations. SIAM J. Numer. Anal. 30(1), 19-39 (1993)
15. Heinrichs, W.: Least-squares spectral collocation for discontinuous and singular perturbation problems. J. Comput. Appl. Math. 157, 329-345 (2003)
16. Heinrichs, W.: Least-squares spectral collocation for the Navier-Stokes equations. J. Sci. Comput. 21(1), 81-90 (2004)
17. Henderson, R.D.: Adaptive spectral element methods for turbulence and transition. In: Earth, T.J., Deconinck, H. (eds.) High Order Methods for Computational Physics, pp. 225-324. Springer, Berlin Heidelberg New York (1999)
18. Jiang, B.-N.: A least-squares finite element method for incompressible Navier-Stokes problems. Int. J. Numer. Methods Fluids 14, 843-859 (1992)
19. Jiang, B.-N.: On the least-squares method. Comput. Methods Appl. Mech. Eng. 152, 239-257 (1998)
20. Jiang, B.-N., Chang, C.L.: Least-squares finite elements for the Stokes problem. Comput. Methods Appl. Mech. Eng. 78, 297-311 (1990)
21. Jiang, B.-N., Povinelli, L.: Least-squares finite element method for fluid dynamics. Comput. Methods Appl. Mech. Eng. 81, 13-37 (1990)
22. Orszag, S.A.: Spectral methods for problems in complex geometries. J. Comput. Phys. 37, 70-92 (1980)
23. Proot, M.J., Gerritsma, M.I.: A least-squares spectral element formulation for the Stokes problem. J. Sci. Comput. 17, 285-296 (2002)
24. Proot, M.J., Gerritsma, M.I.: Least-squares spectral elements applied to the Stokes problem. J. Comput. Phys. 181(2), 454-477 (2002)
25. Proot, M.J., Gerritsma, M.I.: Application of the least-squares spectral element method using Chebyshev polynomials to solve the incompressible Navier-Stokes equations. Numer. Algorithms 38, 155-172 (2005)
26. Rønquist, E.: Optimal spectral element methods for the unsteady three dimensional incompressible Navier-Stokes equations. PhD thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts (1988)