The discrete compactness property for anisotropic edge elements on polyhedral domains
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 1, p. 169-181
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.
DOI : https://doi.org/10.1051/m2an/2012024
Classification:  65N30
Keywords: discrete compactness property, edge elements, anisotropic finite elements, Maxwell equations
@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},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {1},
     year = {2013},
     pages = {169-181},
     doi = {10.1051/m2an/2012024},
     zbl = {1281.78014},
     mrnumber = {2979513},
     language = {en},
     url = {http://www.numdam.org/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, Volume 47 (2013) no. 1, pp. 169-181. doi : 10.1051/m2an/2012024. http://www.numdam.org/item/M2AN_2013__47_1_169_0/

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