报告题目：Convergence of renormalized finite element methods for heat flow of harmonic maps
报告人：王冀鲁，哈尔滨工业大学（深圳）教授
报告时间：2023.05.22下午2:00-3:00
腾讯会议：127-904-093
会议密码：123456
会议链接：//meeting.tencent.com/dm/m6Tp0vfPcVXT
摘要：A linearly implicit renormalized lumped mass finite element method is considered for solving the equations describing heat flow of harmonic maps, of which the exact solution naturally satisfies the pointwise constraint $|\m|=1$. At every time level, the method first computes an auxiliary numerical solution by a linearly implicit lumped mass method and then renormalizes it at all finite element nodes before proceeding to the next time level. It is shown that such a renormalized finite element method has an error bound of $O(\tau+h^{r+1})$ for tensor-product finite elements of degree $r\ge 1$. The proof of the error estimates is based on a geometric relation between the auxiliary and renormalized numerical solutions. The extension of the error analysis to triangular mesh is straightforward and discussed in the conclusion section.
报告人简介：王冀鲁，哈尔滨工业大学（深圳）教授，此前为北京计算科学研究中心特聘研究员。王冀鲁博士的研究兴趣为偏微分方程数值解，包括关于浅水波方程、多孔介质中不可压混溶驱动模型、薛定谔方程以及分数阶方程的数值方法。曾入选国家高层次青年人才计划，目前分别主持和参与国家自然科学基金面上项目和重点项目。
邀请人：杜锐