Alonso, Ana; Russo, AnahĂ Dello Spectral approximation of variationally formulated eigenvalue problems on curved domains. (English) Zbl 1171.65075 ETNA, Electron. Trans. Numer. Anal. 35, 69-87 (2009). Summary: This paper is concerned with the spectral approximation of variationally formulated eigenvalue problems posed on curved domains. As an example of the present theory, convergence and optimal error estimates are proved for the piecewise linear finite element approximation of the eigenvalues and eigenfunctions of a second order elliptic differential operator on a general curved three-dimensional domain. Cited in 2 Documents MSC: 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 35P15 Estimates of eigenvalues in context of PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs Keywords:spectral approximation; eigenvalue problems; curved domains; convergence; optimal error estimates; finite element; eigenfunctions; second order elliptic differential operator PDFBibTeX XMLCite \textit{A. Alonso} and \textit{A. D. Russo}, ETNA, Electron. Trans. Numer. Anal. 35, 69--87 (2009; Zbl 1171.65075) Full Text: EuDML EMIS