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.
@article{M2AN_2013__47_1_169_0,
author = {Lombardi, Ariel Luis},
title = {The discrete compactness property for anisotropic edge elements on polyhedral domains},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {47},
year = {2013},
pages = {169-181},
doi = {10.1051/m2an/2012024},
mrnumber = {2979513},
zbl = {1281.78014},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2013__47_1_169_0}
}
Lombardi, Ariel Luis. The discrete compactness property for anisotropic edge elements on polyhedral domains. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) pp. 169-181. doi : 10.1051/m2an/2012024. http://gdmltest.u-ga.fr/item/M2AN_2013__47_1_169_0/
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