题目：Spectral volume methods for hyperbolic equations

报告人：曹外香 教授，北京师范大学

时间：2025年7月14日（周一）17:00-18:00

地点：东区五教5206

摘要：This talk is concerned with the analysis of two spectral volume (SV) methods for 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 and any polynomial degree $k$, both the LSV and RRSV methods are stable and can achieve optimal convergence orders in the $L^2$ norm. Secondly, we prove that both methods have some superconvergence properties at some special points. For instances, at the downwind points, the solution of RRSV and  LSV methods converges  with the order of ${\cal O}(h^{2k+1})$ and ${\cal O}(h^{2k})$, respectively. Moreover, we demonstrate that for constant-coefficient equations, the RRSV method is identical to the upwind discontinuous Galerkin (DG) method. Our theoretical findings are validated with several numerical experiments at the end.

报告人简介：曹外香，北京师范大学数学科学学院教授，研究方向为偏微分方程数值解法和数值分析，主要研究有限元方法、有限体积方法，间断有限元方法高效高精度数值计算。主要结果发表在SIAM J. Numer. Anal., Math. Comp.等期刊上。曾获中国博士后基金一等资助和特别资助，广东省自然科学二等奖，主持国家自然科学基金面上项目、国家自然科学基金青年基金等项目。