In this paper, we analyze the lower bound property of the discreteeigenvalues by the rectangular Morley elements of the biharmonic operators inboth two and three dimensions. The analysis relies on an identity for theerrors of eigenvalues. We explore a refined property of the canonicalinterpolation operators and use it to analyze the key term in this identity. Inparticular, we show that such a term is of higher order for two dimensions, andis negative and of second order for three dimensions, which causes a maindifficulty. To overcome it, we propose a novel decomposition of the first termin the aforementioned identity. Finally, we establish a saturation condition toshow that the discrete eigenvalues are smaller than the exact ones. We presentsome numerical results to demonstrate the theoretical results.
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