Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Associate Prof. Xuefeng Liu，Niigata University, Japan
Inviter:	谢和虎研究员
Title:	Rigorous and fully computable a posteriori error bounds for eigenfunctions
Time & Venue:	2019.4.30 16:30-17:30 Z305
Abstract:	Guaranteed a posteriori error estimates for eigenfunctions in both energy and $L^2$ norms are derived for the Laplace eigenvalue problem. The problem of ill-conditioning of eigenfunctions in case of tight clusters and multiple eigenvalues issolved by estimating the directed distance between corresponding spaces of eigenfunctions. Also, if there is time, I will give a short report on "Progress about computer-assisted proof for the stationary solution of Navier-Stokes equation" As one of the Millennium Prize Problems, the problem of existence and smoothness of the Navier--Stokes equation draws the attention of mathematician from the world. Meanwhile, the verified computing with assistance of computers has proved to be a promising approach to investigate the solution existence to nonlinear equation systems. In this talk, I will report the latest progress about the solution verification for the stationary Navier--Stokes equation over a non-convex 3D domain.