Polynomial extension operators. Part i

SIAM Journal on Numerical Analysis

Volumn 46, Issue 6, 2008, Pages 3006-3031

  Demkowicz, Leszek ^a   Gopalakrishnan, Jayadeep ^b   Schöberl, Joachim ^c  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF FLORIDA   (United States)

^c RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Extension; Normal; Polynomial; Sobolev; Tangential; Trace

Indexed keywords

EXTENSION; NORMAL; SOBOLEV; TANGENTIAL; TRACE;

COMPUTATIONAL MECHANICS;

POLYNOMIAL APPROXIMATION;

EID: 55349140368     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/070698786     Document Type: Article

References (26)

1. M. AINSWORTG AND L. DEMKOWICZ, Explicit polynomial preserving trace liftings on a triangle, Math. Nachr., to appear.
2. Sec also ICES Report 03-47.
3. I. BABUŠKA, A. CRAIG, J. MANDEL, AND J. PITKÄRANTA, Efficient preconditioning for the p-version finite element method in two dimensions, SIAM J. Numer. Anal., 28 (1991), pp. 624-661.
4. I. BABUŠKA AND M. SURI, The h-p version of the finite element method with quasiuniform meshes, RAIRO Mode'el. Math. Anal. Num'er., 21 (1987), pp. 199-238.
5. F. B. BELGACEM, Polynomial extensions of compatible polynomial traces in three dimensions, Comput. Methods Appl. Mech. Engrg., 116 (1994), pp. 235-241. ICOSAHOM'92 (Montpellier, 1992).
6. C. BERNARDI, M. DAUGE, AND Y. MADAY, Polynomials in the sobolev world, Technical report 07-14, IRMAR, University of Rennes, 2007.
7. A. BUFFA AND P. CIARLET, JR., On traces for functional spaces related to Maxwell's equations. I. An integration by parts formula in Lipschitz polyhedra, Math. Methods Appl. Sci., 24 (2001), pp. 9-30.
8. M. CESSENAT, Mathematical methods in electro-magnetism. Linear theory and applications, Ser. Adv. Math. Appl. Sci. 41, World Scientific Publishing Co. Pte. Ltd., Singapore, 1996.
9. 1, H(curl), and H(div) spaces on a cube, Technical report, IRMAR, Rennes, 2007.
10. L. DEMKOWICZ AND I. BABUŠKA, Optimal p interpolation error estimates for edge finite elements of variable order in two dimensions, SIAM J. Numer. Anal., 41 (2003), pp. 1195-1208 (electronic).
11. 1, H(curl) and H (div)-conforming projection-based interpolation in three dimensions. Quasi-optimal p-interpolation estimates, Comput. Methods Appl. Mech. Engrg., 194 (2005), pp. 267-296.
12. L. DEMKOWICZ, J. GOPALAKRISHNAN, AND J. SCHÖBERL, Polynomial extension operators. Part II, SIAM J. Numer. Anal., submitted.
13. L. DEMKOWICZ, J. GOPALAKRISIINAN, AND J. SOHÖBERL, Polynomial extension operators. Part III, in preparation.
14. L. DEMKOWICZ, Polynomial Exact Sequences and Projection-based Interpolation with Applications to Maxwell Equations, in Mixed Finite Elements, Compatibility Conditions and Applications, D. Boffi and L. Gastaldi, eds., Lecture Notes in Mathematics, Springer-Verlag, 2007. See also ICES Report 06-12.
15. V. GIRAULT AND P.-A. RAVIART, Finite Element Methods for Navier-Stokes Equations, in Springer series in Computational Mathematics 5, Springer-Verlag, New York, 1986.
16. J. GOPALAKRISHNAN AND L. F. DEMKOWICZ, Quasioptimality of some spectral mixed methods, J. Comput. Appl. Math., 167 (2004), pp. 163-182.
17. J. GOPALAKRISHNAN AND J. E. PASCIAK, The convergence of V-cycle multigrid algorithms for axisymmetric Laplace and Maxwell equations, Math. Comp., 75 (2006), pp. 1697-1719.
18. P. GRISVARD, Elliptic Problems in Nonsmooth Domains, in Monographs and Studies in Mathematics 24, Pitman Advanced Publishing Program, Marshfleld, Massachusetts, 1985.
19. N. HEUER AND F. LEYDECKER, An extension theorem for polynomials on triangles, Technical report, BICOM, Brunel University, Uxbridge, UB8 3PH, England, 2005.
20. S. KESAVAN, Topics in Functional Analysis and Applications, Wiley Eastern Limited, Bombay, 1989.
21. A. KUFNER, Weighted Sobolev Spaces, A Wiley-Interscience Publication, John Wiley & Sons Inc., New York, 1985. Translated from the Czech.
22. Y. MADAY, Relèvements de traces polynomials et interpolations hilbertiennes entre espaces de polynômes, C. R. Acad. Sci. Paris. Sér. I Math., 309 (1989), pp. 463-468.
23. Y. MADAY, Analysis of spectral projectors in one-dimensional domains, Math. Comp., 55 (1990), pp. 537-562.
24. W. MCLEAN, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, 2000.
25. 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 (1997), pp. 282-314.
26. J. SCHÖBERL, J. MELENK, C. PECHSTEIN, AND S. ZAGLMAYR, Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements, IMA J. Numer. Anal., 28 (2008), pp. 1-24.