Tetrahedral hp finite elements: Algorithms and flow simulations

Journal of Computational Physics

Volumn 124, Issue 1, 1996, Pages 14-45

  Sherwin, S J ^a   Karniadakis, G E ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

TENSORS;

COMPLEX DOMAINS; DISCRETIZATIONS; FINITE ELEMENT ALGORITHMS; HP-FINITE ELEMENTS; INCOMPRESSIBLE (NAVIER )STOKES EQUATION; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; MODAL BASIS; SPECTRAL ELEMENT; SPECTRAL METHODS; SUBDOMAIN;

NAVIER STOKES EQUATIONS;

EID: 0030096938     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.0042     Document Type: Article

References (34)

1. 1. G. E. Karniadakis and S. A. Orszag, Phys. Today 46, 34 (1993).
2. 2. J. Peraire, K. Morgan, J. Peiro, and O. C. Zienkiewicz, AIAA Paper 87:559, 1987 (unpublished).
3. 3. T. J. Barth, AIAA-93-0668, 1993 (unpublished).
4. 4. R. A. Shapiro and E. M. Murman, AIAA-89-0655 (unpublished).
5. 5. K. Morgan, O. Hassan, and J. Peraire, Int. J. Numer. Methods Fluids 19, 849 (1994).
6. 6. H. Kreiss and J. Olinger, "Methods for the Approximate Solution of Time Dependent Problems," GARP Publ. Ser., Vol. 10, GARP, Geneva, 1973.
7. 7. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications (SIAM-CMBS, Philadelphia, 1977).
8. 8. S. K. Lele, J. Comput. Phys. 103, 16 (1992).
9. 9. A. T. Patera, J. Comput. Phys. 54, 468 (1984).
10. 10. G. E. Karniadakis, E. T. Bullister, and A. T. Patera, "A Spectral Element Method for Solution of Two- and Three-Dimensional Time Dependent Navier-Stokes Equations," in Finite Element Methods for Nonlinear Problems, (Springer-Verlag, New York/Berlin, (1985), p. 803.
11. 11. N. P. Weatherill and O. Hassan, Int. J. Numer. Methods Eng. 37, 2005 (1994).
12. 12. S. J. Sherwin and G. E. Karniadakis, Comput. Methods Appl. Mech. Eng., 123, 189 (1995).
13. 13. S. J. Sherwin and G. E. Karniadakis, Int. J. Numer. Methods Eng., in press.
14. 14. L. Demkowicz, J. T. Oden, W. Rachowicz, and O. Hardy, Comput. Methods Appl. Mech. Eng. 77, 79 (1989).
15. 15. B. Szabo and I. Babuska, Finite Element Analysis (Wiley, New York, 1991).
16. 16. G. E. Karniadakis, M. Israeli, and S. A. Orszag, J. Comput. Phys. 97, 414 (1991).
17. 17. C. Canuto, M. Y. Husanini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer-Verlag, New York/ Berlin, 1988).
18. 18. M. Dubiner, J. Sci. Comput. 6, 345 (1991).
19. 19. S. J. Sherwin and G. E. Karniadakis, "Adaptive hp Finite Elements on Unstructured Meshes," in Finite Elements in Fluids New Trends and Applications, Venice, 1995.
20. 20. T. C. E. Warburton, S. J. Sherwin, and G. E. Karniadakis, "Unstructured hp/Spectral Elements: Connectivity and Optimal," in ICES '95, 1995.
21. 21. T. J. Baker, Appl. Numer. Math. 5, 275 (1989).
22. 22. A. Ghizzetti and A. Ossicini, Quadrature Formulae (Academic Press, New York, 1970).
23. 23. I. Babuska, B. Guo, and M. Suri, Impact Comput. Sci. Eng. 1, 36 (1989).
24. 24. C. Canuto and A. Quarteroni, Math. Comput. 38, 67 (1982).
25. 25. C. Canuto and A. Quarteroni, "Variational Methods in the Theoretical Analysis of Spectral Approximations," in Spectral Methods for Partial Differential Equations, edited by R. G. Voight, D. Gottlieb, and M. Y. Hussaini (SIAM, Philadelphia, 1984), p. 55.
26. 26. Y. Maday and E. M. Ronquist, "Optimal Error Analysis of Spectral Methods with Emphasis on Non-constant Coefficient and Deformed Geometries," in Spectral and High Order Methods for Partial Differential Equations, edited by C. Canuto and A. Quarteroni (North-Holland, 1989), p. 91.
27. 27. E. O. Macagno and T. Hung, J. Fluid Mech. 28, 43 (1967).
28. 28. D. J. Newman and G. E. Karniadakis, unpublished report, Brown University, 1994.
29. 29. R. D. Henderson and G. E. Karniadakis, J. Comput. Phys., in press.
30. 30. C. G. Lewis and M. Gharib, Phys. Fluid A 4, 104 (1992).
31. 31. M. W. M. Ko and A. S. K. Chan, Exp. Fluids 104, 213 (1990).
32. 32. P. S. Piccirillo and C. W. Van Atta, J. Fluid Mech. 246, 163 (1993).
33. 33. C. H. K. Williamson, J. Fluid Mech. 243, 393 (1992).
34. 34. S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods (Springer-Verlag, New York, 1994).