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The discrete compactness property for anisotropic edge elements on polyhedral domains. (English) Zbl 1281.78014
The author proves the validity of the discrete compactness property for edge elements of any order on a class of anisotropically refined tetrahedral meshes on general Lipschitz polyhedral domains. Both edge and corner refinements are considered. The class of meshes considered includes the anisotropic graded meshes designed by T. Apel and S. Nicaise [Math. Methods Appl. Sci. 21, No. 6, 519–549 (1998; Zbl 0911.65107)].
MSC:
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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