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We consider a model eigenvalue problem (EVP) in 1D, with
periodic or semi–periodic boundary conditions (BCs). The discretization of
this type of EVP by consistent mass finite element methods (FEMs) leads to
the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric
matrices, with a certain (skew–)circulant structure. In this paper we fix our
attention to the use of a quadratic FE–mesh. Explicit expressions for the
eigenvalues of the resulting algebraic EVP are established. This leads...
We deal with a class of elliptic eigenvalue problems (EVPs)
on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions
(BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational
formulation which is shown to fit into the general framework of abstract
EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert
spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs)
without and with numerical quadrature. The aim of the paper is...
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