Energy stability and error analysis of a maximum bound principle preserving scheme for the dynamical Ginzburg-Landau equations of superconductivity
数学专题报告
报告题目(Title)：Energy stability and error analysis of a maximum bound principle preserving scheme for the dynamical Ginzburg-Landau equations of superconductivity
报告人(Speaker)：乔中华教授（香港理工大学）
地点(Place)：后主楼1124
时间(Time)：2023年3月16日(周四), 10：00-11:00
邀请人(Inviter)：张争茹
报告摘要
We focus on numerical study of the dynamical Ginzburg-Landau equations under the temporal gauge, and propose a decoupled numerical scheme based on the finite element method. For the variable A, the second type Nedelec element is employed for the space discretization and the backward Euler is applied for the time discretization where the nonlinear term is treated explicitly. For the order parameter, the first order exponential time differencing method is employed with the linear operator generated by the linear element method with lumping. The proposed numerical scheme is proved to preserve the discrete maximum bound principle for the order parameter and admit an unconditional energy decay property. An optimal error estimate is also given for the scheme which is verified by the numerical examples.
主讲人简介
乔中华博士于2006年在香港浸会大学获得博士学位，现为香港理工大学应用数学系教授。
乔博士主要从事数值微分方程方面算法设计及分析，近年来研究工作集中在相场方程的数值模拟及计算流体力学的高效算法。他至今在SCI期刊上发表论文70余篇，文章被合计引用1700余次。他于2013年获香港研究资助局颁发2013至2014年度杰出青年学者奖，于2018年获得香港数学会青年学者奖，并且于2020年获得香港研究资助局研究学者奖。
