Computable upper and lower bounds on eigenfrequencies

This paper is a revisit of the work [Ladevèze and Pelle, Int. J. Numer. Methods Engrg. 28 (1989)] where the goal here is to acquire guaranteed, accurate and computable bounds of eigenfrequencies through post-processing of conventional finite element results. To this end, a new theoretical quotient is introduced and thereafter, a practical way to deal with the new quotient is developed where the constitutive relation error estimation featured with guaranteed bounding property acts as a key role. Academic numerical examples are performed to check the accuracy of the bounds.