The discrete compactness property for anisotropic edge elements on polyhedral domains∗

Ariel Luis Lombardi

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 47, Issue: 1, page 169-181
  • ISSN: 0764-583X

Abstract

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We prove the discrete compactness property of the edge elements of any order on a class of anisotropically refined meshes on polyhedral domains. The meshes, made up of tetrahedra, have been introduced in [Th. Apel and S. Nicaise, Math. Meth. Appl. Sci. 21 (1998) 519–549]. They are appropriately graded near singular corners and edges of the polyhedron.

How to cite

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Lombardi, Ariel Luis. "The discrete compactness property for anisotropic edge elements on polyhedral domains∗." ESAIM: Mathematical Modelling and Numerical Analysis 47.1 (2012): 169-181. <http://eudml.org/doc/222148>.

@article{Lombardi2012,
abstract = {We prove the discrete compactness property of the edge elements of any order on a class of anisotropically refined meshes on polyhedral domains. The meshes, made up of tetrahedra, have been introduced in [Th. Apel and S. Nicaise, Math. Meth. Appl. Sci. 21 (1998) 519–549]. They are appropriately graded near singular corners and edges of the polyhedron.},
author = {Lombardi, Ariel Luis},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Discrete compactness property; edge elements; anisotropic finite elements; Maxwell equations; discrete compactness property},
language = {eng},
month = {8},
number = {1},
pages = {169-181},
publisher = {EDP Sciences},
title = {The discrete compactness property for anisotropic edge elements on polyhedral domains∗},
url = {http://eudml.org/doc/222148},
volume = {47},
year = {2012},
}

TY - JOUR
AU - Lombardi, Ariel Luis
TI - The discrete compactness property for anisotropic edge elements on polyhedral domains∗
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/8//
PB - EDP Sciences
VL - 47
IS - 1
SP - 169
EP - 181
AB - We prove the discrete compactness property of the edge elements of any order on a class of anisotropically refined meshes on polyhedral domains. The meshes, made up of tetrahedra, have been introduced in [Th. Apel and S. Nicaise, Math. Meth. Appl. Sci. 21 (1998) 519–549]. They are appropriately graded near singular corners and edges of the polyhedron.
LA - eng
KW - Discrete compactness property; edge elements; anisotropic finite elements; Maxwell equations; discrete compactness property
UR - http://eudml.org/doc/222148
ER -

References

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  13. P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford University Press, New York (2003).  Zbl1024.78009
  14. P. Monk and L. Demkowicz, Discrete compactness and the approximation of Maxwell’s equations in R3. Math. Comp.70 (2001) 507–523.  Zbl1035.65131
  15. J.C. Nédélec, Mixed finite elements in R3. Numer. Math.35 (1980) 315–341.  Zbl0419.65069
  16. S. Nicaise, Edge elements on anisotropic meshes and approximation of the Maxwell equations. SIAM J. Numer. Anal.39 (2001) 784–816.  Zbl1001.65122
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  18. Ch. Weber, A local compactness theorem for Maxwell’s equations. Math. Meth. Appl. Sci.2 (1980) 12–25.  Zbl0432.35032

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