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Mathematics of Computation

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Eigenvalue approximation by the finite element method: the method of Lagrange multipliers

Author: William G. Kolata
Journal: Math. Comp. 33 (1979), 63-76
MSC: Primary 65N25; Secondary 65N30
MathSciNet review: 514810
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Abstract: The purpose of this paper is to investigate the application of the finite element method of Lagrange multipliers to the problem of approximating the eigenvalues of a selfadjoint elliptic operator satisfying Dirichlet boundary conditions. Although the Lagrange multiplier method is not a Rayleigh-Ritz-Galerkin approximation scheme, it is shown that at least asymptotically the Lagrange multiplier method has some of the properties of such a scheme. In particular, the approximate eigenvalues are greater than or equal to the exact eigenvalues and can be computed from a nonnegative definite matrix problem. It is also shown that the known estimates for the eigenvalue error are optimal.

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Keywords: Finite element method, Lagrange multipliers, selfadjoint elliptic eigenvalue problems
Article copyright: © Copyright 1979 American Mathematical Society