报告题目：An Implicit-Explicit Relaxation Extrapolated Runge-Kutta and Energy-Preserving Finite Element Method for Klein-Gordon-Schrodinger Equations

报告人：姚昌辉

报告时间：2024年07月28日（周日）上午11:00开始

报告地点：数学楼315会议室

报告摘要：An implicit-explicit (IMEX) relaxation extrapolated Runge-Kutta (RERK) and energy-preserving finite element method is designed for Klein-Gordon-Schr\"{o}dinger (KGS) equations with periodic boundary conditions. First, the RERK method is employed to the discretization in temporal, in order to keep the unconditionally stable and energy conservation by selecting the appropriate relaxation parameters $\gamma_n$. An IMEX time-marching discretization is constructed so that it need to be solved with only one linear equations in any time step. Next, the finite element method is utilized to the discretization in spatial. By the temporal-spatial splitting technique, optimal error estimates in the $L^2$-norm and $H^1$-norm are obtained with the convergent order $\mathcal{O}(\tau^{s}+h^{k+1})$ and $\mathcal{O}(\tau^{s}+h^{k})$, without any time stepsize restrictions. At last, some numerical examples are presented to demonstrate the theoretical results.

报告人简介：姚昌辉，博士、教授，博士生导师。中国数学会计算数学分会常务理事，中国仿真学会不确定性系统分析与仿真专业委员会常务委员。2006年6月在中国科学院获得计算数学专业理学博士学位， 2008在挪威Bergen大学获得应用数学专业哲学博士学位。主要从事基于能量分析的电磁场高效有限元数值模拟， 曾主持国家自然科学基金青年基金1项，国家自然科学基金面上项目2项，2021年出版河南省“十四五”普通高等教育规划教材《数值分析》，2022年获得由河南省人民政府颁发的自然科学奖二等奖。