Free Access
Issue
ESAIM: M2AN
Volume 46, Number 2, November-December 2012
Page(s) 239 - 263
DOI https://doi.org/10.1051/m2an/2011042
Published online 12 October 2011
  1. D.N. Arnold, R.S. Falk and R. Winther, Finite element exterior calculus, homological techniques, and applications. Acta Num. 15 (2006) 1–155. [CrossRef] [MathSciNet] [Google Scholar]
  2. D.N. Arnold, R.S. Falk and R. Winther, Finite element exterior calculus: from Hodge theory to numerical stability. Bull. Am. Math. Soc. 47 (2010) 281–354. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Bergot, G. Cohen and M. Duruflé, Higher-order finite elements for hybrid meshes using new nodal pyramidal elements. J. Sci. Comput. 42 (2010) 345–381. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.H. Bramble and S.R. Hilbert, Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIAM J. Numer. Anal. 7 (1970) 112–124. [CrossRef] [MathSciNet] [Google Scholar]
  5. S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods. Springer Verlag (2008). [Google Scholar]
  6. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. Society for Industrial Mathematics (2002). [Google Scholar]
  7. J.L. Coulomb, F.X. Zgainski and Y. Maréchal, A pyramidal element to link hexahedral, prismatic and tetrahedral edge finite elements. IEEE Trans. Magn. 33 (1997) 1362–1365. [CrossRef] [Google Scholar]
  8. L. Demkowicz and A. Buffa, H1, Formula and Formula -conforming projection-based interpolation in three dimensions. Quasi-optimal Formula -interpolation estimates. Comput. Methods Appl. Mech. Eng. 194 (2005) 267–296. [Google Scholar]
  9. L. Demkowicz, J. Kurtz, D. Pardo, M. Paszenski and W. Rachowicz, Computing with hp-Adaptive Finite Elements Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications 2. Chapman & Hall (2007). [Google Scholar]
  10. M. Fortin and F. Brezzi, Mixed and Hybrid Finite Element Methods (Springer Series in Computational Mathematics). Springer-Verlag Berlin and Heidelberg GmbH & Co. K (1991). [Google Scholar]
  11. V. Gradinaru and R. Hiptmair, Whitney elements on pyramids. Electronic Transactions on Numerical Analysis 8 (1999) 154–168. [MathSciNet] [Google Scholar]
  12. R.D. Graglia and I.L. Gheorma, Higher order interpolatory vector bases on pyramidal elements. IEEE Trans. Antennas Propag. 47 (1999) 775. [CrossRef] [Google Scholar]
  13. P.C. Hammer, O.J. Marlowe and A.H. Stroud, Numerical integration over simplexes and cones. Mathematical Tables Aids Comput. 10 (1956) 130–137. [CrossRef] [Google Scholar]
  14. J.M. Melenk, K. Gerdes and C. Schwab, Fully discrete hp-finite elements: Fast quadrature. Comput. Methods Appl. Mech. Eng. 190 (2001) 4339–4364. [CrossRef] [Google Scholar]
  15. P. Monk, Finite element methods for Maxwell's equations. Numerical Mathematics and Scientific Computation. Oxford University Press, New York (2003). [Google Scholar]
  16. J.-C. Nedéléc, Mixed finite elements in Formula . Num. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet] [Google Scholar]
  17. N. Nigam and J. Phillips, High-order conforming finite elements on pyramids. IMA J. Numer. Anal. (2011); doi: 10.1093/imanum/drr015. [Google Scholar]
  18. A.H. Stroud, Approximate calculation of multiple integrals. Prentice-Hall Inc., Englewood Cliffs, N.J. (1971). [Google Scholar]
  19. J. Warren, On the uniqueness of barycentric coordinates, in Topics in Algebraic Geometry and Geometric Modeling: Workshop on Algebraic Geometry and Geometric Modeling, July 29-August 2, 2002, Vilnius University, Lithuania. American Mathematical Society 334 (2002) 93–99. [Google Scholar]
  20. C. Wieners, Conforming discretizations on tetrahedrons, pyramids, prisms and hexahedrons. Technical report, University of Stuttgart. [Google Scholar]
  21. S. Zaglmayr, High Order Finite Element methods for Electromagnetic Field Computation. Ph. D. thesis, Johannes Kepler University, Linz (2006). [Google Scholar]
  22. F.-X. Zgainski, J.-L. Coulomb, Y. Marechal, F. Claeyssen and X. Brunotte, A new family of finite elements: the pyramidal elements. IEEE Trans. Magn. 32 (1996) 1393–1396. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you