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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.
@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 },
pages = {169--181},
publisher = {EDP-Sciences},
volume = {47},
number = {1},
year = {2013},
doi = {10.1051/m2an/2012024},
mrnumber = {2979513},
zbl = {1281.78014},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012024/}
}
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 PY - 2013 SP - 169 EP - 181 VL - 47 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012024/ DO - 10.1051/m2an/2012024 LA - en ID - M2AN_2013__47_1_169_0 ER -
%0 Journal Article %A Lombardi, Ariel Luis %T The discrete compactness property for anisotropic edge elements on polyhedral domains %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 169-181 %V 47 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012024/ %R 10.1051/m2an/2012024 %G en %F 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 , Tome 47 (2013) no. 1, pp. 169-181. doi: 10.1051/m2an/2012024
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