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Vanmaele, M.; Van Keer, Roger

An operator method for a numerical quadrature finite element approximation for a class of second-order elliptic eigenvalue problems in composite structures. (English) Zbl 0836.65113

RAIRO, Modélisation Math. Anal. Numér. 29, No. 3, 339-365 (1995).
The authors consider a second-order elliptic eigenvalue problem on a two- dimensional convex polygonal domain, divided in \(M\) non-overlapping subdomains. The conormal derivative of the unknown function is continuous on the interfaces, while the function itself is discontinuous. The authors study the finite element approximation without and with numerical quadrature.
The method developed by the authors in an earlier paper is refined and extended to the multicomponent structure with discontinuities on the interfaces. Rectangular mesh is admitted, as well as finite elements of higher degree. A nonstandard variational formulation of the eigenvalue problem is used. The authors emphasize the error analysis of the approximate eigenpairs.
Reviewer: P.Burda (Praha)

Cited in 1 Review
Cited in 10 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
65N15 Error bounds for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs

Keywords:

multicomponent domain; operator method; second-order elliptic eigenvalue problem; finite element; numerical quadrature; error analysis
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Full Text: DOI EuDML

References:

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