Geodesic
Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem
Serdica Mathematical Journal, Tome 25 (1999) no. 2, pp. 177-184.

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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 to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].
Keywords: Eigenvalue Problems, Periodic Boundary Conditions, Circulant Matrices 
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     author = {De Schepper, H.},
     title = {Some {Computational} {Aspects} of the {Consistent} {Mass} {Finite} {Element} {Method} for a (semi-)periodic {Eigenvalue} {Problem}},
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De Schepper, H. Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem. Serdica Mathematical Journal, Tome 25 (1999) no. 2, pp. 177-184. http://geodesic.mathdoc.fr/item/SMJ2_1999_25_2_a5/