EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 56 / No 3 (May-June 2022) ESAIM: M2AN, 56 3 (2022) 867-891 References
Open Access
Issue
ESAIM: M2AN
Volume 56, Number 3, May-June 2022
Page(s) 867 - 891
DOI https://doi.org/10.1051/m2an/2022009
Published online 25 April 2022
  1. I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids. Comput. Geosci. 6 (2002) 405–432. [CrossRef] [MathSciNet] [Google Scholar]
  2. I. Aavatsmark, Interpretation of a two-point flux stencil for skew parallelogram grids. Comput. Geosci. 11 (2007) 199–206. [CrossRef] [Google Scholar]
  3. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics Series. Vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC (1964). [Google Scholar]
  4. I. Ambartsumyan, E. Khattatov, J.J. Lee and I. Yotov, Higher order multipoint flux mixed finite element methods on quadrilaterals and hexahedra. Math. Models Methods Appl. Sci. 29 (2019) 1037–1077. [CrossRef] [MathSciNet] [Google Scholar]
  5. D.N. Arnold and G. Awanou, Finite element differential forms on cubical meshes. Math. Comp. 83 (2014) 1551–1570. [Google Scholar]
  6. D.N. Arnold, R.S. Falk and R. Winther, Finite element exterior calculus, homological techniques, and applications. Acta Numer. 15 (2006) 1–155. [Google Scholar]
  7. D.N. Arnold, R.S. Falk and R. Winther, Finite element exterior calculus: from Hodge theory to numerical stability. Bull. Amer. Math. Soc. (N.S.) 47 (2010) 281–354. [Google Scholar]
  8. D.N. Arnold, D. Boffi and F. Bonizzoni, Finite element differential forms on curvilinear cubic meshes and their approximation properties. Numer. Math. 129 (2015) 1–20. [CrossRef] [MathSciNet] [Google Scholar]
  9. J. Baranger, J.-F. Maitre and F. Oudin, Connection between finite volume and mixed finite element methods. RAIRO: M2AN 30 (1996) 445–465. [CrossRef] [EDP Sciences] [Google Scholar]
  10. M. Bause, J. Hoffmann and P. Knabner, First-order convergence of multi-point flux approximation on triangular grids and comparison with mixed finite element methods. Numer. Math. 116 (2010) 1–29. [CrossRef] [MathSciNet] [Google Scholar]
  11. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Series in Computational Mathematics. Vol. 15. Springer (1992). [Google Scholar]
  12. F. Brezzi, M. Fortin and L.D. Marini, Error analysis of piecewise constant pressure approximations of Darcy’s law. Comput. Methods Appl. Mech. Eng. 195 (2006) 1547–1559. [CrossRef] [Google Scholar]
  13. S.H. Christiansen and A. Gillette, Constructions of some minimal finite element systems. ESAIM: M2AN 50 (2016) 833–850. [CrossRef] [EDP Sciences] [Google Scholar]
  14. B. Cockburn and W. Qiu, Commuting diagrams for the TNT elements on cubes. Math. Comp. 83 (2014) 603–633. [Google Scholar]
  15. G. Cohen and P. Monk, Gauss point mass lumping schemes for Maxwell’s equations. Numer. Methods Part. Differ. Equ. 14 (1998) 63–88. [CrossRef] [Google Scholar]
  16. M. Desbrun, A.N. Hirani, M. Leok and J.E. Marsden, Discrete exterior calculus. Preprint arXiv:math/0508341 (2005). [Google Scholar]
  17. J. Droniou and R. Eymard, A mixed finite volume scheme for anisotropic diffusion problems on any grid. Numer. Math. 105 (2006) 35–71. [Google Scholar]
  18. A. Gillette and T. Kloefkorn, Trimmed serendipity finite element differential forms. Math. Comp. 88 (2019) 583–606. [Google Scholar]
  19. R. Hiptmair, Discrete Hodge operators. Numer. Math. 90 (2001) 265–289. [CrossRef] [MathSciNet] [Google Scholar]
  20. A.N. Hirani, Discrete exterior calculus. Ph.D. thesis, California Institute of Technology ProQuest LLC, Ann Arbor, MI (2003). [Google Scholar]
  21. R. Ingram, M.F. Wheeler and I. Yotov, A multipoint flux mixed finite element method on hexahedra. SIAM J. Numer. Anal. 48 (2010) 1281–1312. [CrossRef] [MathSciNet] [Google Scholar]
  22. R.A. Klausen and R. Winther, Convergence of multipoint flux approximations on quadrilateral grids. Numer. Methods Part. Differ. Equ. 22 (2006) 1438–1454. [CrossRef] [Google Scholar]
  23. R.A. Klausen and R. Winther, Robust convergence of multi point flux approximation on rough grids. Numer. Math. 104 (2006) 317–337. [CrossRef] [MathSciNet] [Google Scholar]
  24. J.J. Lee and R. Winther, Local coderivatives and approximation of Hodge Laplace problems. Math. Comp. 87 (2018) 2709–2735. [CrossRef] [MathSciNet] [Google Scholar]
  25. E. Schulz and G. Tsogtgerel, Convergence of discrete exterior calculus approximations for Poisson problems. Discrete Comput. Geom. 63 (2020) 346–376. [CrossRef] [MathSciNet] [Google Scholar]
  26. M. Vohralik and B.I. Wohlmuth, Mixed finite element methods: implementation with one unknown per element, local flux expressions, positivity, polygonal meshes, and relations to other methods. Math. Models Methods Appl. Sci. 23 (2013) 803–838. [Google Scholar]
  27. M.F. Wheeler and I. Yotov, A multipoint flux mixed finite element method. SIAM J. Numer. Anal. 44 (2006) 2082–2106. [CrossRef] [MathSciNet] [Google Scholar]
  28. M. Wheeler, G. Xue and I. Yotov, A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra. Numer. Math. 121 (2012) 165–204. [CrossRef] [MathSciNet] [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