Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Associate Prof. Xuefeng Liu，Niigata University, Japan
Rigorous and fully computable a posteriori error bounds for eigenfunctions
Time & Venue:
2019.4.30 16:30-17:30 Z305
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.
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