We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue
problem. By using the special nonconforming finite elements, ie, enriched Crouzeix-Raviart
element and extended Q 1 rot, we get the lower bound of the eigenvalue. Additionally, we
use conforming finite elements to do the postprocessing to get the upper bound of the
eigenvalue, which only needs to solve the corresponding source problems and a small
eigenvalue problem if higher order postprocessing method is implemented. Thus, we can …

摘要 We introduce some ways to compute the lower and upper bounds of the Laplace
eigenvalue problem. By using the special nonconforming finite elements, ie, enriched
Crouzeix-Raviart element and extended Q (1)(rot), we get the lower bound of the
eigenvalue. Additionally, we use conforming finite elements to do the postprocessing to get
the upper bound of the eigenvalue, which only needs to solve the corresponding source
problems and a small eigenvalue problem if higher order postprocessing method is …