报告题目：Analysis of a class of spectral volume method for linear scalar conservation laws
报 告 人：卢键方 副教授 （华南理工大学）
报告时间：2024年6月22日， 周六 上午 10:30-11:30
报告地点：数学学院207
邀 请 人：宋怀玲
报告摘要：In this talk, we will study a class of spectral volume (SV) method for the hyperbolic conservation laws in the Petrov-Galerkin framework. It is well known that the SV method is equivalent to the discontinuous Galerkin (DG) method with an appropriate choice of the subdivision points, therefore it is natural to analyze the SV method in the Galerkin form and derive the analogous theoretical results as in DG method. Inspired by [Cao-Zou-JSC2022], we consider a class of subdivision points, which are the zeros of a specific polynomial with a parameter in it. We present the information of the zeros of the given polynomial, and investigate some properties of the piecewise constant functions under this subdivision, including the orthogonality between the trial solution space and test function space. With the aid of these properties, we are able to derive the energy stability, optimal a priori error estimates and superconvergence. Particularly, we adopt the correction function technique [Cao-Zhang-Zou-SINUM2014] to obtain the superconvergence of the numerical solution, and show the order of superconvergence will be different with different choice of the subdivision points, coincided with the results given in [Cao-Zou-JSC2022]. In the numerical experiments, by choosing different parameters in the SV method, the theoretical findings are confirmed by the numerical results.
报告人简介：卢键方博士，（华南理工大学）。卢键方博士于2010年在中国科学技术大学获得理学学士学位，2016年博士毕业于中国科学技术大学，2016至2018年在北京计算科学研究中心做博士后；随后在华南数学应用与交叉研究中心做青年英才，2021年至今，华南理工大学副教授，研究领域为计算流体力学和非局部方程的数值方法。
欢迎老师和同学们参加！
