汇报标题 (Title)：Caputo-Hadamard分数演化方程的移动网格有限元步骤
汇报人 (Speaker)：樊恩宇 讲师（内蒙古大学）
汇报功夫 (Time)：2026年5月22日（周五）16:00
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：李常品、蔡敏
主办部门：理学院数学系
汇报提要：This report aims to numerically solve the blow-up solution to the semi-linear Caputo-Hadamard fractional evolution equation. Firstly, the moving mesh finite element scheme is established to solve the linear Caputo-Hadamard fractional evolution equation which has a sharp solution, where the L1 formula is used for time fractional derivative. The numerical stability, convergence, and error estimates for the fully discrete scheme are analyzed. And the numerical scheme is successfully used to solve the sharp solution to the linear problem. Then, based on the method and technique, the moving mesh finite element method is built up for the semi-linear problem. The numerical simulations show that the derived fully discrete scheme is efficient and effective for solving the finite time blow-up solution to the semi-linear Caputo-Hadamard fractional evolution equation. And the numerical experiments disclose the fact that blow-up time increases when the fractional derivative order increases.
