Explicit polynomial preserving trace liftings on a triangle

Mathematische Nachrichten

Volumn 282, Issue 5, 2009, Pages 640-658

  Ainsworth, Mark ^a   Demkowicz, Leszek ^b  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Domain decomposition; p Version finite element method; Polynomial extension; Polynomial lifting; Spectral element method; Trace lifting

Indexed keywords

EID: 67449139023     PISSN: 0025584X     EISSN: 15222616     Source Type: Journal    
DOI: 10.1002/mana.200610762     Document Type: Article

References (24)

1. R. A. Adams, Sobolev Spaces, Pure and Applied Mathematics Vol. 65 (Academic Press, New York - London, 1975).
2. M. Ainsworth and B. Guo, An additive Schwarz preconditioner for p-version boundary element approximation of the hypersingular operator in three dimensions, Numer. Math. 85, 343-366 (2000).
3. 2, SIAM J. Numer. Anal. 28, 624-661 (1991).
4. I. Babuska and M. Suri, The h-p version of the finite element method with quasi-uniform meshes, RAIRO Modél. Math. Anal. Numér. 21, 199-238 (1987).
5. F. Ben Belgacem, Polynomial extensions of compatible polynomial traces in three dimensions, in: Proceedings of the ICOSAHOM'92, Montpellier 1992, Computer Methods in Applied Mechanics Engineering Vol. 116 (North-Holland, Amsterdam -New York, 1994), pp. 235-241.
6. J. Bergh and J. Löfström, Interpolation Spaces (Springer-Verlag, Berlin - Heidelberg, 1976).
7. C. Bernardi, M. Dauge, and Y. Maday, Relèvements de traces préservant les polynômes, C. R. Acad. Sci. Paris Sér. I Math. 315, 333-338 (1992).
8. 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 Non-smooth Domains, edited by M. Costabel, M. Dauge, and S. Nicaise, Lecture Notes in Pure and Applied Mathematics Vol. 167 (Marcel Dekker Inc., New York, 1995), pp. 27-46.
9. C. Bernardi and Y. Maday, Relèvement polynomial de traces et applications, RAIRO Modél. Math. Anal. Numér. 24, 557-611 (1990).
10. R. P. Boas, Jr. and C. O. Imoru, Elementary convolution inequalities, SIAM J. Math. Anal. 6, 457-471 (1975).
11. J. Bramble, J. Pasciak, and A. Schatz, The construction of preconditioners for elliptic problems by substructuring I, Math. Comp. 47, 103-135 (1986).
12. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods (Springer-Verlag, Berlin, 1991).
13. L. Demkowicz and I. Babuška, p-interpolation error estimates for edge finite elements of variable order in two dimension, SIAM J. Numer. Anal. 41, 1195-1208 (2003).
14. M. Dryja and O. B.Widlund, Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems, Comm. Pure Appl. Math. 48, 121-155 (1995).
15. E. Gagliardo, Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili, Rend. Sem. Mat. Univ. Padova 27, 284-305 (1957).
16. P. Grisvard, Elliptic Problems in Non-smooth Domains, Monographs and Studies in Mathematics Vol. 24 (Pitman, London, 1985).
17. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge Mathematical Library (Cambridge University Press, Cambridge, 1988), reprint of the 1952 edition.
18. J.-L. Lions, Théorèmes de trace et d'interpolation. IV, Math. Ann. 151, 42-56 (1963).
19. J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications - I, Grundlehren der Mathematischen Wissenschaften Bd. 181 (Springer-Verlag, Berlin -New York, 1972).
20. Y. Maday, Relèvements de traces polynomiales et interpolations hilbertiennes entre espaces de polynômes, C. R. Acad. Sci. Paris Sér. I Math. 309, 463-468 (1989).
21. V. G. Maz'ja, Sobolev Spaces, Springer Series in Soviet Mathematics, translated from the Russian by T. O. Shaposhnikova (Springer-Verlag, Berlin, 1985).
22. R. Muñoz-Sola, Polynomial liftings on a tetrahedron and applications to the h-p version of the finite element method in three dimensions, SIAM J. Numer. Anal. 34, 282-314 (1997).
23. E. Sawyer, Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator, Trans. Amer. Math. Soc. 281, 329-337 (1984).
24. G. Sinnamon, A weighted gradient inequality, Proc. Roy. Soc. Edinburgh Sect. A 111, 329-335 (1989).