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Isoparametric finite-element approximation of a Steklov eigenvalue problem. (English) Zbl 1069.65120
Authors’ abstract: We study the isoparametric variant of the finite element method (FEM) for an approximation of Steklov eigenvalue problems for second-order, selfadjoint, elliptic differential operators. Error estimates for eigenfunctions and eigenvalues are derived. We prove the same estimate for eigenvalues as that obtained in the ease of conforming finite elements provided that the boundary of the domain is well approximated. Some algorithmic aspects arising from the FEM isoparametric discretization of the Steklov problems are analysed. We finish the paper with numerical results confirming the considered theory.

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
65N15 Error bounds for boundary value problems involving PDEs
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