報告題目：A class of efficient Hamiltonian conservative spectral methods for Korteweg-de Vries equation
報 告 人：曹外香 副教授 北京師範大學
報告時間：2022年0 7月08日 星期五 10:00-11:00
報告地點：騰訊會議 ID: 169-740-404
校内聯系人：王翔 wxjldx@jlu.edu.cn
報告摘要：In this talk, we present and introduce two efficient Hamiltonian conservative fully discrete numerical schemes for Korteweg-de Vries equations. The new numerical schemes are constructed by using time-stepping spectral Petrov-Galerkin (SPG) or Gauss collocation (SGC) methods for the temporal discretization coupled with the $p$-version/spectral local discontinuous Galerkin (LDG) methods for the space discretization. We prove that the fully discrete SPG-LDG scheme preserves both the momentum and the Hamilton energy exactly for generalized KdV equations. While the fully discrete SGC-LDG formulation preserves the momentum and the Hamilton energy exactly for linearized KdV equations. As for nonlinear KdV equations, the SGC-LDG scheme preserves the momentum exactly and is Hamiltonian conserving up to some spectral accuracy. Furthermore, we show that the semi-discrete $p$-version LDG methods converge exponentially with respect to the polynomial degree. The numerical experiments are provided to demonstrate that the proposed numerical methods preserve the momentum, $L^2$ energy and Hamilton energy and maintain the shape of the solution phase efficiently over long time period.
報告人簡介： 曹外香，北京師範大學數學科學學院副教授，美國布朗大學訪問學者，研究方向為偏微分方程數值解法和數值分析，主要研究有限元方法、有限體積方法，間斷有限元方法高效高精度數值計算。主要結果發表在SIAM J. Numer. Anal., Math. Comp., J. Sci. Comput. 等期刊上。曾獲中國博士後基金一等資助和特别資助，廣東省自然科學二等獎，主持國家自然科學基金面上項目、國家自然科學基金青年基金等項目。
