学术报告预告(主讲人:曹外香,时间:4月11日)

作者: 时间:2023-04-04 点击数:

报告题目A class of efficient Hamiltonian conservative spectral methods for Korteweg-de Vries equations

报告时间2023411日(星期),15:00-16:00

报告地点:腾讯会议116 535 741

内容摘要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.

报告人简介:曹外香,北京师范大学数学科学学院副教授,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., J. Sci. Comput., J. Comput. Phys. 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青年基金一项,面上项目两项。


欢迎感兴趣的老师和同学参加!

                                   数学与系统科学学院



地址:广州市天河区中山大道西293号 香港最全资料图库数学与系统科学学院(510665)  电话:020-36540569、38265770 邮箱:[email protected]