Stable spectral methods on tetrahedral elements

SIAM Journal on Scientific Computing

Volumn 21, Issue 6, 2000, Pages 2352-2380

  Hesthaven, J S ^a   Teng, C H ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

JACOBI POLYNOMIALS; SPECTRAL METHODS; TETRAHEDRAL ELEMENTS;

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; ELECTROSTATICS; POLYNOMIALS; PROBLEM SOLVING; TENSORS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0034503732     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827598343723     Document Type: Article

References (24)

1. A. PATERA, A spectral element method for fluid dynamics: Laminar flow in a channel expansion, J. Comput. Phys., 54 (1984), pp. 468-488.
2. J. S. HESTHAVEN, A stable penalty method for the compressible Navier-Stokes equations. III. Multidimensional domain decomposition schemes, SIAM J. Sci. Comput., 20 (1998), pp. 62-93.
3. I. BABUŠKA AND M. SURI, The p-and h - p versions of the finite element method, an overview, Comput. Methods Appl. Mech. Engrg., 80 (1990), pp. 5-20.
4. S. J. SHERWIN AND G. E. KARNIADAKIS, Tetrahedral hp finite elements: Algorithms and flow simulations, J. Comput. Phys., 124 (1996), pp .14-45.
5. B. A. WINGATE AND M. A. TAYLOR, The Natural Function Space for Triangular and Tetrahedral Spectral Elements, manuscript.
6. M. DUBINER, Spectral methods on triangles and other domains, J. Sci. Comput., 6 (1991), pp. 345-390.
7. J. PRORIOL, Sur une famille de polynomes à deux variables orthogonaux dans un triangle, C. R. Acad. Sci. Paris, 245 (1957), pp. 2459-2461.
8. T. KOORNWINDER, Two-variable analogues of the classical orthogonal polynomials, in Theory and Application of Special Functions, R.A. Askey, ed., Academic Press, New York, 1975. pp. 435-495.
9. Q. CHEN AND I. BABUŠKA, Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle, Comput. Methods Appl. Mech. Engrg., 128 (1995), pp. 405-417.
10. Q. CHEN AND I. BABUSKA, The optimal symmetrical points for polynomial interpolation of real functions in a tetrahedron, Comput. Methods Appl. Mech. Engrg., 137 (1996), pp. 89-94.
11. J. S. HESTHAVEN, Prom electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex, SIAM J. Numer. Anal., 35 (1998), pp. 655-676.
12. M. A. TAYLOR AND B. A. WINGATE, Fekete collocation points for triangular spectral elements, SIAM J. Numer. Anal., submitted.
13. M. H. CARPENTER AND D. GOTTLIEB, Spectral methods on arbitrary grids, J. Comput. Phys., 129 (1996), pp. 74-86.
14. J. S. HESTHAVEN AND D. GOTTLIEB, Stable spectral methods for conservation laws on triangles with unstructured grids, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 361-381.
15. O. C. ZIENKIEWICZ AND R. L. TAYLOR, The Finite Element Method. Volume 1. Basic Formulation and Linear Problems, 4th ed., McGraw-Hill, London, 1989.
16. K. C. CHUNG AND T. H. YAO, On lattices admitting unique Lagrange interpolations, SIAM J. Numer. Anal., 14 (1977), pp. 735-743.
17. L. P. BOS, Bounding the Lebesgue Function for Interpolation in a Simplex, J. Approx. Theory, 38 (1983), pp. 43-59.
18. G. SZEGÖ, Orthogonal Polynomials, American Mathematical Society Colloquium Publications 23, AMS, New York, 1939.
19. E. HAIRER, S. P. NØRSETT, AND G. WANNER, Solving Ordinary Differential Equations I, Springer Ser. Comput. Math. 8, Springer-Verlag, Berlin, 1989.
20. J. S. HESTHAVEN, A stable penalty method for the compressible Navier-Stokes equations. II. One-dimensional domain decomposition schemes, SIAM J. Sci. Comput., 18 (1997), pp. 658-685.
21. A. SOLOMONOFF, A fast algorithm for spectral differentiation, J. Comput. Phys., 98 (1992), pp. 174-177.
22. H. O. KREISS AND L. WU, On the stability definition of difference approximations for the initial boundary value problem, Appl. Numer. Math., 12 (1993), pp. 213-227.
23. J. S. HESTHAVEN AND D. GOTTLIEB, A stable penalty method for the compressible Navier-Stokes equations. I. Open boundary conditions, SIAM J. Sci. Comput., 17 (1996), pp. 579-612.
24. G. E. KARNIADAKIS, private communication, 1998.