an:04145270
Zbl 0698.65067
Kikuchi, Fumio
On a discrete compactness property for the Nedelec finite elements
EN
J. Fac. Sci., Univ. Tokyo, Sect. I A 36, No. 3, 479-490 (1989).
00173528
1989
j
65N30 35J25 78A30
divergence conditions; electromagnetic problems; Nedelec finite elements; discrete compactness; stability; convergence
It is shown that the simplest Nedelec finite elements [cf. \textit{J.-C. Nedelec}, Numer. Math. 35, 315-341 (1980; Zbl 0419.65069)] in \(R^ 2\) and \(R^ 3\) satisfy a kind of discrete compactness property under some assumptions on the considered domain. This property may be effectively employed to guarantee the stability and the convergence of the finite element solutions.
The results were partially announced by the author in Comput. Methods Appl. Mech. Eng. 64, 509-521 (1987; Zbl 0644.65087).
W.Moldenhauer
Zbl 0419.65069; Zbl 0644.65087