Convergence and stability of a numerical method for micromagnetics

The convergence and stability of a numerical method, which applies a nonconforming finite element method and an artificial boundary method to a multi-atomic Young measure relaxation model, for micromagnetics are analyzed. By revealing some key properties of the solution sets of both the continuous and discrete problems, we show that our numerical method is stable, and the solution set of the continuous problem is well approximated by those of the discrete problems. The performance of our method is also illustrated by some numerical examples. The research was supported in part by the Major State Basic Research Projects (2005CB321701), NSFC projects (10431050, 10571006, 10528102 and 10871011) and RFDP of China.