Reduction of finite element subspace dimension based on estimated error

This paper examines the idea of basing dimensional reduction for finite element subspaces on estimated error. Orthonormal bases related to the error terms in a quadratic error estimator are established by solving algebraic eigenvalue problems, to identify components most suitable for deletion from finite element subspaces. Error-based eigenvectors are compared with less expensive vibration eigenvectors for two example problems. It is found that vibration eigenvectors correlate very well with error-based eigenvectors, so that optimal dimensional reduction can be approximated very well using traditional modal truncation. In addition, results indicate that substantial participation of higher vibration eigenvectors in a finite element approximation can be indicative of a high level of error.