Natural frequency error estimation using a patch recovery technique

In computing eigenvalues for a large finite element system, it has been observed that the eigenvalue extractors produce eigenvectors that are in some sense more accurate than their corresponding eigenvalues. In this paper, computational examples are presented to validate this observation. From this observation, a patch type technique is developed based on the eigenvector for one mesh quality to provide an eigenvalue error indicator. Tests show this indicator to be both accurate and reliable. This technique was first observed by Stephen and Steven for an error estimation for buckling and has been extended in this paper to predict an error for the natural frequency finite element analysis of a structure. (C) 1997 Academic Press Limited.