Spectral approximation of variationally-posed eigenvalue problems by nonconforming methods (Q953382)

The goal of this paper is to obtain some abstract results of spectral approximation that can be applied to a wide class of nonconforming methods for compact or noncompact operators. The consistency results derived by the authors are extensions of the results developed by \textit{J. Descloux , N. Nassif} and \textit{J. Rappaz} [RAIRO, Anal. Numér. 12, 97--112 (1978; Zbl 0393.65024); ibid. 12, 113--119 (1978; Zbl 0393.65025)]. The theory presented here allows the analysis of a large class of discontinuous finite element methods when they are used for the approximation of spectral problems. Two representative eigenvalue elliptical problems are discussed in detail: the Steklov eigenvalue problem (in which the eigenvalue parameter appears in the boundary condition) and an eigenvalue problem for a system of partial differential equations. The analysis is carried out for the lowest order Crouzeix-Raviart finite element space.