Abstract
The eigenvalues of a fourth order, generalized eigenvalue problem in one dimension, with non-smooth coefficients are approximated by a finite element method, introduced in an earlier work by the author and A. Lutoborski, in the context of a similar source problem with non-smooth coefficients. Error estimates for the approximate eigenvalues and eigenvectors are obtained, showing a better performance of this method, when applied to eigenvalue approximation, compared to a standard finite element method with arbitrary mesh.
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Banerjee, U. Approximation of the eigenvalues of a fourth order differential equation with non-smooth coefficients. BIT 31, 620–631 (1991). https://doi.org/10.1007/BF01933177
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DOI: https://doi.org/10.1007/BF01933177