报告题目：Convergence of renormalized finite element methods for heat flow of harmonic maps

报告时间：2024-04-30   14:30-15:30

报 告 人 ： 王冀鲁教授   哈尔滨工业大学（深圳）

报告地点：腾讯会议 520 596 846

Abstract：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 Ο(τ+h^r+1) for tensor-product finite elements of degree r≥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.