Finding eigenvalues of operators is important in the mathematical sciences. Many numerical methods have been used to approximate eigenvalue problems of partial differential operators, such as finite difference methods, finite element methods and spectral methods.However, it is well-known that when finite difference methods and finite element methods are applied, only a small portion of numerical eigenvalues can be reliable. Is it possible to improve accuracy for a large number of eigenvalues?
Adaptive finite element methods has been widely used to improve the accuracy of numerical solutions of PDE problems including PDE eigenvalue problems. It is believed to be one of the most efficient discretizations. Is it possible to improve largely adaptive finite element methods of PDE eigenvalue problems?
This talk will try to touch the aforementioned topics.