## 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

## 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.## References

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## Additional Information

- © Copyright 1979 American Mathematical Society
- Journal: Math. Comp.
**33**(1979), 63-76 - MSC: Primary 65N25; Secondary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-1979-0514810-0
- MathSciNet review: 514810