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 Optimal error estimates of renormalized finite element methods for heat flow of harmonic maps and related problems

主讲人：王冀鲁

摘要：A linearly implicit renormalized lumped mass finite element method is considered for solving the equations describing heat flow of harmonic maps and related problems, 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.

主讲人简介：王冀鲁，哈尔滨工业大学（深圳）教授，国家高层次青年人才，此前为北京计算科学研究中心特聘研究员。王冀鲁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。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：李东方

时间： 2025年9月11日18:00-20:00

地点：  腾讯会议室： 175210324