Polynomial extension operators. Part II

SIAM Journal on Numerical Analysis

Volumn 47, Issue 5, 2009, Pages 3293-3324

  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 trace; Polynomial; Sobolev; Tangential

Indexed keywords

COMMUTATIVITY PROPERTIES; ELEMENT ANALYSIS; EXTENSION; EXTENSION OPERATORS; HIGH ORDER; NORMAL TRACE; SOBOLEV; TANGENTIAL; TRACE FUNCTIONS;

COMPUTATIONAL MECHANICS;

POLYNOMIALS;

EID: 70350143470     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/070698798     Document Type: Article

References (19)

1. A. Alonso and A. Valli, Some remarks on the characterization of the space of tangential traces of H(rot;U) and the construction of an extension operator, Manuscripta Math., 89 (1996), pp. 159-178.
2. J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer-Verlag, New York, 1976.
3. C. Bernardi, Optimal finite-element interpolation on curved domains, SIAM J. Numer. Anal., 26 (1989), pp. 1212-1240.
4. A.-S. Bonnet-Ben Dhia, C. Hazard, and S. Lohrengel, A singular field method for the solution of Maxwell's equations in polyhedral domains, SIAM J. Appl. Math., 59 (1999), pp. 2028-2044 (electronic).
5. 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.
6. A. Buffa and P. Ciarlet, Jr., On traces for functional spaces related to Maxwell's equations. II. Hodge decompositions on the boundary of Lipschitz polyhedra and applications, Math. Methods Appl. Sci., 24 (2001), pp. 31-48.
7. L. Demkowicz and A. Buffa, H1, 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.
8. L. Demkowicz, J. Gopalakrishnan, and J. Schöberl, Polynomial Extension Operators. Part III, manuscript, 2007.
9. L. Demkowicz, J. Gopalakrishnan, and J. Schöberl, Polynomial extension operators. Part I, SIAM J. Numer. Anal., 46 (2008), pp. 3006-3031.
10. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer Ser. Comput. Math. 5, Springer-Verlag, New York, 1986.
11. J. Gopalakrishnan and L. F. Demkowicz, Quasioptimality of some spectral mixed methods, J. Comput. Appl. Math., 167 (2004), pp. 163-182.
12. P. Grisvard, Elliptic Problems in Nonsmooth Domains, Monogr. Stud. Math. 24, Pitman, Marshfield, MA, 1985.
13. J. L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications, Vol.I, Springer-Verlag, New York, 1972.
14. P. Monk, Finite Element Methods for Maxwell's Equations, Numer. Math. Sci. Comput., Oxford University Press, New York, 2003.
15. J.-C. Nédélec, Mixed finite elements in R3, Numer. Math., 35 (1980), pp. 315-341.
16. J. E. Pasciak and J. Zhao, Overlapping Schwarz methods in H(curl) on polyhedral domains, J. Numer. Math., 10 (2002), pp. 221-234.
17. J. Peetre, Nouvelles propriétés d'espaces d'interpolation, C. R. Acad. Sci. Paris, 256 (1963), pp. 1424-1426.
18. 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.
19. E. M. Stein, Singular Integrals and differentiability Properties of Functions, Princeton Math. Ser. 30, Princeton University Press, Princeton, NJ, 1970.