Open Access
Issue
ESAIM: M2AN
Volume 56, Number 6, November-December 2022
Page(s) 2239 - 2253
DOI https://doi.org/10.1051/m2an/2022088
Published online 08 December 2022
  1. R. Abraham, J.E. Marsden and T. Ratiu, Manifolds, Tensor Analysis, and Applications. Vol. 75, Springer Science & Business Media (2012). [Google Scholar]
  2. A. Alonso Rodrguez, L. Bruni Bruno and F. Rapetti, Minimal sets of unisolvent weights for high order whitney forms on simplices, in Numerical Mathematics and Advanced Applications ENUMATH 2019. Springer (2021) 195–203. [Google Scholar]
  3. A. Alonso Rodríguez, L. Bruni Bruno and F. Rapetti, Flexible weights for high order face based finite element interpolation. Submitted (2022). [Google Scholar]
  4. A. Alonso Rodríguez, L. Bruni Bruno and F. Rapetti, Towards nonuniform distributions of unisolvent weights for Whitney finite element spaces on simplices: the edge element case. Calcolo 59 (2022). [PubMed] [Google Scholar]
  5. R. Anderson, J. Andrej, A. Barker, J. Bramwell, J.-S. Camier, J. Cerveny, V. Dobrev, Y. Dudouit, A. Fisher, T. Kolev, W. Pazner, M. Stowell, V. Tomov, I. Akkerman, J. Dahm, D. Medina and S. Zampini, MFEM: a modular finite element methods library. Comput. Math. App. 81 (2021) 42–74. Development and Application of Open-source Software for Problems with Numerical PDEs. [Google Scholar]
  6. A. Apozyan, Ǵ. Avagyan and G. Ktryan, On the Gasca-Maeztu conjecture in ℝ3. East J. Approx. 16 (2010) 25–33. [MathSciNet] [Google Scholar]
  7. D. Arnold, R. Falk and R. Winther, Finite element exterior calculus, homological techniques, and applications. Acta Numer. 15 (2006) 1–155. [CrossRef] [MathSciNet] [Google Scholar]
  8. V. Bayramyan, H. Hakopian and S. Toroyan, A simple proof of the Gasca-Maeztu conjecture for n = 4. Jaen J. Approx. 7 (2015) 137–147. [MathSciNet] [Google Scholar]
  9. M. Bonazzoli and F. Rapetti, High-order finite elements in numerical electromagnetism: degrees of freedom and generators in duality. Numer. Algor. 74 (2017) 111–136. [Google Scholar]
  10. A. Bossavit, Computational Electromagnetism: Variational Formulations, Complementarity. Edge Elements. Academic Press Inc., San Diego, CA (1998). [Google Scholar]
  11. A. Bossavit and L. Kettunen, Yee-like schemes on staggered cellular grids: a synthesis between FIT and FEM approaches. IEEE Trans. Magn. 36 (2000) 861–867. [Google Scholar]
  12. F. Brezzi, J. Douglas and L.D. Marini, Two families of mixed finite elements for second order elliptic problems. Numer. Mathem. 47 (1985) 217–235. [Google Scholar]
  13. L. Bruni Bruno, Weights as degrees of freedoom for high order Whitney finite elements. Ph.D. thesis, University of Trento (2022). [Google Scholar]
  14. J.M. Carnicer and M. Gasca, A conjecture on multivariate polynomial interpolation. RACSAM. Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat. 95 (2001) 145–153. [Google Scholar]
  15. S.H. Christiansen, A construction of spaces of compatible differential forms on cellular complexes. Math. Models Methods Appl. Sci. 18 (2008) 739–757. [Google Scholar]
  16. S.H. Christiansen, Foundations of finite element methods for wave equations of Maxwell type, in Applied Wave Mathematics. Springer (2009) 335–393. [CrossRef] [Google Scholar]
  17. S.H. Christiansen and F. Rapetti, On high order finite element spaces of differential forms. Math. Comput. 85 (2016) 517–548. [Google Scholar]
  18. S. Christiansen, H. Munthe-Kaas and B. Owren, Topics in structure preserving discretization. Acta Numer. 20 (2011) 1–119. [CrossRef] [MathSciNet] [Google Scholar]
  19. K.C. Chung and T.H. Yao, On lattices admitting unique Lagrange interpolations. SIAM J. Numer. Anal. 14 (1977) 735–743. [Google Scholar]
  20. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland Publishing Co (1978). [Google Scholar]
  21. C. de Boor, Multivariate polynomial interpolation: conjectures concerning GC-sets. Numer. Algorithms 45 (2007) 113–125. [Google Scholar]
  22. M. Gasca and J.I. Maeztu, On Lagrange and Hermite interpolation in ℝk. Numer. Math 39 (1982) 1–14. [Google Scholar]
  23. J. Gopalakrishnan, L.E. Garca-Castillo and L.F. Demkowicz, Nédélec spaces in affine coordinates. Comput. Math. Appl. 49 (2005) 1285–1294. [CrossRef] [MathSciNet] [Google Scholar]
  24. H. Hakopian, K. Jetter and G. Zimmermann, The Gasca-Maeztu conjecture for n = 5. Numer. Math. 127 (2014) 685–713. [Google Scholar]
  25. J. Harrison, Continuity of the integral as a function of the domain. J. Geometric Anal. 8 (1998) 769–795. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Hatcher, Algebraic Topology. Cambridge Univ. Press, Cambridge (2000). [Google Scholar]
  27. R. Hiptmair, Canonical construction of finite elements. Math. Comp. 68 (1999) 1325–1346. [Google Scholar]
  28. L. Kettunen, J. Lohi, J. Räbinä, S. Mönkölä and T. Rossi, Generalized finite difference schemes with higher order Whitney forms. ESAIM: Math. Model. Numer. Anal. 55 (2021) 1439–1459. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  29. J.M. Lee, Introduction to Smooth Manifolds. Vol. 218 of Graduate Texts in Mathematics, 2nd edition. Springer (2012). [CrossRef] [Google Scholar]
  30. J. Lohi, Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus. Numer. Algorithms 91 (2022) 1261–1285. [Google Scholar]
  31. J.-C. Nédélec, Mixed finite elements in ℝ3. Numer. Math. 35 (1980) 315–342. [Google Scholar]
  32. J.-C. Nédélec, A new family of mixed finite elements in ℝ3. Numer. Math. 50 (1986) 57–81. [Google Scholar]
  33. R.A. Nicolaides, On a class of finite elements generated by Lagrange interpolation. SIAM J. Numer. Anal. 9 (1972) 435–445. [Google Scholar]
  34. F. Rapetti and A. Bossavit, Whitney forms of higher degree. SIAM J. Numer. Anal. 47 (2009) 2369–2386. [Google Scholar]
  35. T. Tarhasaari, L. Kettunen and A. Bossavit, Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques [for EM field analysis]. IEEE Trans. Magn. 35 (1999) 1494–1497. [CrossRef] [Google Scholar]
  36. H. Whitney, Geometric Integration Theory. Princeton University Press (1957). [Google Scholar]
  37. E. Zampa, A. Alonso Rodríguez and F. Rapetti, Using the F.E.S. framework to derive new physical degrees of freedom for Nédélec spaces in two dimensions. Submitted (2021). [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