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This is a survey article about using non-conforming finite elements in solving eigenvalue problems of elliptic operators,
with emphasis on obtaining lower bounds. In addition, this article also contains some new materials for eigenvalue approximations
of the Laplace operator, which include: 1) the proof of the fact that the non-conforming Crouzeix-...
We study the n-simplex nonconforming Crouzeix-Raviart element in approximating the n-dimensional second-order elliptic boundary value problems and the associated eigenvalue problems. By using the second Strang Lemma, optimal rate of convergence is established under the discrete energy norm. The error bound is also valid for the eigenfunction approx...