Zhimin Zhang, Professor, Wayne State University

Zhongzhi Bai, Professor

How Many PDE Numerical Eigenvalues Can We Trust, and How to Get More Out of It?

10:00-11:00 October 2 (Sunday), Tencent Meeting ID: 359-771-916

When approximating PDE eigenvalue problems by numerical methods such as finite difference and finite element, it is common knowledge that only a small portion of numerical eigenvalues are reliable. However, this knowledge is only qualitative rather than quantitative in the literature. In this talk, we will investigate the number of “trusted” eigenvalues by the finite element (and the related finite difference method results obtained from mass lumping) approximation of 2mth order elliptic PDE eigenvalue problems. Our two model problems are the Laplace and bi-harmonic operators, for which a solid knowledge regarding magnitudes of eigenvalues are available in the literature. Combining this knowledge with a priori error estimates of the finite element method, we are able to figure out roughly how many “reliable” eigenvalues can be obtained from numerical approximation under a pre-determined convergence rate.