On the number of reliable finite-element eigenmodes

Abstract

The finite-element (FE) approximation of linear elliptic eigenvalue problems is considered. An analysis based on a number of known estimates leads to the simple formula M=r0ed/(2p)N relating the total number of degrees of freedom N, the maximum relative error level e desired for the eigenvalues, and the number of ‘reliable’ modes M. (Here d is the spatial dimension and p is the polynomial degree of the FE space.) Moreover, a rough estimate for the numerical value of the constant r0 for a given application is found. This result supports a well-known rule of thumb. Copyright © 2008 John Wiley & Sons, Ltd.