Polynomial liftings on a tetrahedron and applications to the h-p version of the finite element method in three dimensions

SIAM Journal on Numerical Analysis

Volumn 34, Issue 1, 1997, Pages 282-314

  Munoz Sola, Rafael ^a  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Finite element method; H p version; Polynomial liftings

Indexed keywords

EID: 0002943819     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994267552     Document Type: Article

References (29)

1. I. BABUŠKA AND M. SURI, The optimal convergence rate of the p version of the finite element method, SIAM J. Numer. Anal., 24 (1987), pp. 750-776.
2. I. BABUŠKA AND M. SURI, The h - p version of the finite element method with quasi-uniform meshes, KAIRO Modél. Math. Anal. Numér., 21 (1987). pp. 199-238.
3. I. BABUŠKA, A. CRAIG. J. MANDEL, AND J. PITKARANTA, Efficient preconditioning for the p-version finite element method in two dimensions, SIAM J. Numer. Anal., 28 (1991), pp. 624-661.
4. I. BABUŠKA, R. B. KELLOG, AND J. PITKARANTA, Direct and inverse error estimates for finite elements with mesh refinements, Numer. Math., 33 (1979), pp. 447-471.
5. F. BEN BELGACEM, Relèvements polynômiaux sur un cube. Direction des Études et Recherches, Electricité de France, Clamart, France, HI-72/7780, 1992.
6. F. BEN BELGACEM, Polynomial extensions of compatible polynomial traces in three dimensions, Comput. Methods Appl. Mech. Engrg., 116 (1994). pp. 235-241.
7. C. BERNARDI AND Y. MADAY. Relèvement polynomial de traces et application, RAIRO Modél. Math. Anal. Numér., 24 (1990). pp. 557-611.
8. C. BERNARDI, Y. MADAY. AND A. T. PATERA, A new nonconforming approach, to domain decomposition: The mortar element method, in Nonlinear Partial Differential Equations and Their Applications. Collège de France Seminar. Vol. XI. Pitman Res. Notes Math. Ser., Vol. 299. Longman Sci. Tech., Harlow. U.K., 1994, pp. 13-51.
9. C. BERNARDI, M. DAUGE, AND Y. MADAY, Relèvements de traces préservant les polynômes, C. R. Acad. Sci. Paris Sér. I Math., 315 (1992). pp. 333-338.
10. C. BERNARDI, M. DAUGE. AND Y. MADAY, Polynomials in weighted Sobolev spaces: Basics and trace liftings, Publications du Laboratoire d'Analyse Numérique, Univ. Pierre et Marie Curie, Paris, Vol. 11, fasc. 7, R92039, 1992.
11. C. BERNARDI, M. DAUGE. AND Y. MADAY. Interpolation of nullspaces for polynomial approximation of divergence-free functions in a cube, in Boundary Value Problems and Integral Equations in Nonsmooth Domains, Lecture Notes in Pure and Appl. Math., Vol. 167, Dekker, New York, 1095, pp. 27-46.
12. I. BERGH AND J. LÖFSTROM, Interpolation Spaces. Springer-Verlag, Berlin, Heidelberg, New York, 1976.
13. P. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
14. M. DAUGE, Problèmes aux limites elliptiques sur den domaines à coins: regularité, indice, estimations, C. R. Acad. Sci. Paris Sér. I Math., 304 (1987), pp. 515-518.
15. M. DAUGE, Problèmes aux limites elliptiques sur des domaines à coins: singularités aux sommets et le long des arêtes, C. R. Acad. Sci. Paris Sér. I Math., 304 (1987), pp. 563-566.
16. M. DAUGE. Elliptic Boundary Value. Problems on Comer Domains, Lecture Notes in Math., Vol. 1341, Springer-Verlag, Berlin, New York, 1988.
17. M. R, DORR, The approximation theory for the p-version of the finite element method. SIAM J. Numer. Anal., 21 (1984), pp. 1180-1207.
18. M. R. DORR, The approximation of solutions of elliptic boundary-value problems via the p-version of the finite element method. SIAM. J. Numer. Anal., 23 (1986), pp. 58-77.
19. E. GAGLIARDO, Caratterizzazioni delle traces sulla frontiera relative, ad alcune classi di funzioni in n variabili, Rend. Sem. Mat. Univ. Padova. 27 (1957). pp. 284-305.
20. P. GRISVARD, Elliptic Problems in Nonsmooth Domains. Pitman, London, 1985.
21. P. GRISVARD, Caractérisation de quelques espaces d'interpolation. Arch. Rational Mech. Anal., 25 (1967), pp. 10-63.
22. P. GRISVARD. Edge behavior of the solution of an elliptic problem, Math. Nachr., 132 (1987), pp. 281-299.
23. P. GRISVARD, Alternative de Fredholm relative au problème de Dirichlet dans un polyèdre, Ann. Scuola Norm. Sup. Pisa Ser. IV, 2 (1975), pp. 359-388.
24. P. GRISVARD, Behavior of the solution of an elliptic boundary value problem in a polygonal or a polyhedral domain, in Numerical Solution of Partial Differential Equations-III SYNSPADE, B. Hubbard, ed., Academic Press, New York, 1975, pp. 207-274.
25. 2 error for the p-version of the finite element method over polygonal domains, Comput. Methods Appl. Mech. Engrg., 97 (1992), pp. 233-243.
26. Y. MADAY, Analysis of spectral projectors in one-dimensional domains. Math. Comp., 55 (1990), pp. 537-562.
27. Y. MADAY, Relèvements de traces polynômiales et interpolations hilbertiennes entre espaces de polynômes, C. R. Acad. Sci. Paris Sér. I Math., 309 (1989), pp. 463-468.
28. T. v. PETERSDORFF AND E. P. STEPHAN, Decompositions in edge and corner singularities for the solution of the Dirichlet problem of the laplacian in a polyhedron, Math. Nachr., 149 (1990). pp. 71-103.
29. 3 and boundary elements on graded meshes, Math. Methods Appl. Sci., 12 (1990), pp. 229-249.