# On the mass matrix spectrum bounds of Wathen and the local moving finite elements of Baines

@inproceedings{Miller1992OnTM,
title={On the mass matrix spectrum bounds of Wathen and the local moving finite elements of Baines},
author={Keith Miller},
year={1992}
}
Andrew Wathen has shown that the eigenvalues of the diagonally-preconditioned piecewise linear moving finite element (MFE) or finite element (FE) mass matrix in n dimensions lie in $[\frac{1}{2},1 + \frac{1}{2}n]$. Baines, using similar considerations, has designed “very local” MFE methods with block-diagonal mass matrices. In this paper a simplified proof of Wathen’s basic spectrum bound is given. It results from a simple comparison bound between the $L^2$ norm and a certain “diagonal norm… CONTINUE READING

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