報(bào)告題目：A class of efficient Hamiltonian conservative spectral methods for Korteweg-de Vries equations
報(bào)告時(shí)間：2023年4月11日（星期二），15:00-16:00
報(bào)告地點(diǎn)：騰訊會(huì)議116 535 741
內(nèi)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.
報(bào)告人簡(jiǎn)介：曹外香，北京師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院副教授，研究方向?yàn)槠⒎址匠虜?shù)值解法和數(shù)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(shù)值計(jì)算。主要結(jié)果發(fā)表在SIAM J. Numer. Anal., Math. Comp., J. Sci. Comput., J. Comput. Phys. 等期刊上。曾獲中國博士后基金一等資助和特別資助，廣東省自然科學(xué)二等獎(jiǎng)，主持國家自然科學(xué)基金青年基金一項(xiàng)，面上項(xiàng)目?jī)身?xiàng)。
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