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In a very recent paper (Hu et al., The lower bounds for eigenvalues of elliptic operators by nonconforming finite element methods, Preprint, 2010), we prove that the eigenvalues by the nonconforming finite element methods are smaller than the exact ones for the elliptic operators. It is well-known that the conforming finite element methods produce the eigenvalues above to the exact ones. In this paper,...
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