A stochastic finite element method for real eigenvalue problems

A stochastic finite element method (SFEM) based on local averages of a random vector field is developed for both distinct and repeated eigenvalues. Formulae for the variances and covariances of the eigenvalues and eigenvectors are derived. It is shown in a numerical example that, as the number of elements increases, solutions obtained from the present SFEM formulation converge much faster than those obtained from the SFEM formulation based on mid-point discretization.