Adaptive Finite Element Method For The Stray Field Equation In Micromagnetism Problems

Micromagnetism is a discipline that studies the magnetization and magnetic moment distribution characteristics of ferromagnetic materials in the nanometer or micrometer scale.To date,micromagnetic simulation has become an important tool for predicting the magnetic properties of real nanomagnets of different sizes,shapes and magnetic materials.This paper designs an adaptive finite element method for two-dimensional and three-dimensional stray field equations in micromagnetic problems,including using a posteriori error estimation based on Polynomial preserving recovery(PPR)and a posteriori error estimation based on Super convergent cluster recovery(SCR),and compared the two posterior error estimations through numerical experiments.Nu-merical experiments show that SCR also has superconvergence in three dimensions for the first time,the results show that the adaptive finite element method based on these two posteriori error estimations is reliable and effective for solving stray field equations in micromagnetic problems.