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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Eigenvalue approximation by the finite element method: the method of Lagrange multipliers
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by William G. Kolata PDF
Math. Comp. 33 (1979), 63-76 Request permission


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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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Math. Comp. 33 (1979), 63-76
  • MSC: Primary 65N25; Secondary 65N30
  • DOI:
  • MathSciNet review: 514810