Guaranteed eigenvalue bounds for the Steklov eigenvalue problem
Provides guaranteed eigenvalue bounds for a class of problems where existing methods fail due to positive definiteness constraints, benefiting researchers in numerical analysis and PDEs.
The authors propose an enhanced eigenvalue estimation algorithm for the Steklov problem that removes the positive definiteness requirement, using Crouzeix-Raviart FEM with quantitative error estimation. Numerical experiments on square and L-shaped domains validate the precision of computed eigenvalue bounds.
To provide mathematically rigorous eigenvalue bounds for the Steklov eigenvalue problem, an enhanced version of the eigenvalue estimation algorithm developed by the third author is proposed, which removes the requirements of the positive definiteness of bilinear forms in the formulation of eigenvalue problems. In practical eigenvalue estimation, the Crouzeix--Raviart finite element method (FEM) along with quantitative error estimation is adopted. Numerical experiments for eigenvalue problems defined on a square domain and an L-shaped domain are provided to validate the precision of computed eigenvalue bounds.