, Volume 61, Issue 1, pp 145-152

A note on the effect of numerical quadrature in finite element eigenvalue approximation

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In a recent work by the author and J.E. Osborn, it was shown that the finite element approximation of the eigenpairs of differential operators, when the elements of the underlying matrices are approximated by numerical quadrature, yield optimal order of convergence when the numerical quadrature satisfies a certain precision requirement. In this note we show that this requirement is indeed sharp for eigenvalue approximation. We also show that the optimal order of convergence for approximate eigenvectors can be obtained, using numerical quadrature with less precision.

The author would like to thank Prof. I. Babuška for several helpful discussions. This work was done during the author's visit to the Institute of Physical Sciences and Technology and the Department of Mathematics of University of Maryland, College Park, MD 20742, USA, and was supported in part by the Office of Naval Research under Naval Research Grant N0001490-J-1030