Lower bounds on the eigenvalues by Crouzeix-Raviart finite elements

• Date: 5. 12. 2024
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Tomáš Vejchodský

In this talk, we will explain how to compute lower bounds on eigenvalues of the Laplace eigenvalue problem by the Crouzeix-Raviart finite element method. Computing estimates on eigenvalues of elliptic operators from below is a challenging task that requires elaborated methods and often some a priori knowledge about the exact spectrum. However, in the case of the Laplace operator, the elliptic projector coincides with the Crouzeix-Raviart interpolation operator, and we can explicitly obtain the corresponding interpolation constant. These special properties enable us to compute accurate lower bounds on eigenvalues easily.