Analysis of spectral volume methods for hyperbolic equations

讲座时间 Datetime: 2021年7月1日，星期四， 15:30-17:00

地点 Venue: 海琴2号楼 A457

报告人 Speaker:  邹青松 教授

单位 Affiliation: 中山大学

报告摘要 Abstract:

In this talk, we will present the theoretical analysis of two spectral volume(SV) methods for 1D scalar hyperbolic equations :one is constructed basing on the Gauss-Legendre points (LSV) and the other is based on the right-Radau points (RRSV).

We first prove that for a general nonuniform mesh, both the LSV and RRSV are stable and can achieve optimal convergence orders in the $L^2$ space.Secondly, we prove that both methods have some superconvergence properties at certain special points. For instances, at the downwind points,RRSV and LSV converge with the order of ${\cal O}(h^{2k+1})$, and the order of ${\cal O}(h^{2k})$, respectively.Moreover, we demonstrate that for constant-coefficient equation, the RRSV method is  identical to the upwind discontinuous Galerkin (DG) method.Our theoretical findings are validated with several numerical experiments .