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Optimal spectral approximation in linearized plate theory. (English) Zbl 0645.35002

Spectral methods are frequently used to replace a partial differential equation posed over an open set in \(R^ 3\) by a series of partial differential equations posed over an open set of lower dimension and which are thus easier to approximate. In the framework of three- dimensional linearized elasticity those methods have already been used to derive two-dimensional approximate models for plates and one-dimensional approximate models for beams. The object of this paper is to show how to construct the “best” Galerkin spectral approximation for thin clamped plates, possibly multi-layered, made of homogeneous or of non-homogeneous materials. To this end, we use a technique introduced by M. Vogelius and I. Babuška.
Reviewer: B.Miara

MSC:

35A35 Theoretical approximation in context of PDEs
35C20 Asymptotic expansions of solutions to PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74B05 Classical linear elasticity
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