| Issue |
ESAIM: M2AN
Volume 47, Number 1, January-February 2013
|
|
|---|---|---|
| Page(s) | 169 - 181 | |
| DOI | https://doi.org/10.1051/m2an/2012024 | |
| Published online | 31 August 2012 | |
The discrete compactness property for anisotropic edge elements on polyhedral domains∗
1
Instituto de Ciencias, Universidad Nacional de General Sarmiento,
J.M. Gutierrez 1150, Los
Polvorines, B1613 GSX Provincia de
Buenos Airesn, Argentina
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2
Departamento de Matemática, Facultad de Ciencias Exactas y
Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Member of CONICET,
Argentina
Received:
28
July
2011
Revised:
29
February
2012
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.
Mathematics Subject Classification: 65N30
Key words: Discrete compactness property / edge elements / anisotropic finite elements / Maxwell equations
Supported by ANPCyT (grant PICT 2010-1675 and PICTO 2008-00089) and by CONICET (grant PIP 11220090100625).
© EDP Sciences, SMAI, 2012
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