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Maxwell eigenvalues and discrete compactness in two dimensions. (English) Zbl 0998.78011
The discete compactness results for a general class of $$hp$$ finite elements is proved (the $$hp$$ finite elements were introducted previously by L. Demkowicz et al. [Meth. Appl. Mech. Engin. 152, 103-124 (1998; Zbl 0994.78011)]). The $$h$$-convergence of 2D elements is discussed only. The proof is based on the extension of Kikuchi’s discrete compactness argument to edge elements of arbitrary order. The use of the inverse inequality is avoided.

##### MSC:
 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 78M25 Numerical methods in optics (MSC2010) 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
##### Keywords:
$$hp$$-finite elements
2Dhp90
Full Text:
##### References:
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