Speaker: Wang Lilian, Professor, Nanyang Technological University

Date: November 22, 2022

Time: 10:00

Location: Tencent Meeting

Sponsor: School of Mathematics, Shandong University

Abstract:

It is known that the accuracy and performance of a usual spectral method might be deleteriously degraded when the solution exhibits local singular behaviors with very limited reqularity. In practice, the sinaularity may occur in many problems under various scenarios such as PDEs in nonsmooth computational domains with sharp corners or with degenerate or discontinuous coefficients, non-matching boundary conditions, singular kernels or potentials, and non-differentiable nonlinear terms among others. In this talk, we shall elaborate on the evolution of spectral methods from the traditional Legendre/Chebyshev methods to Jacobi polynomials, generalised Jacobi polynomials (GJPs), and generalised Jacobi functions (GJFs), and present fundamental spectral approximation theory of Jacobi approximation to typical singular solutions under fractional Sobolev framework. We then develop fast and accurate spectral algorithms for various singular and nonlocal problems and problems with highly oscillatory solutions.

For more information, please visit:

http://www.math.sdu.edu.cn/info/1020/17995.htm