Numerical analysis of an explicit approximation scheme for the Landau-Lifshitz-Gilbert equation
Sören Bartels, Joy Ko, Andreas Prohl · Mathematics of Computation · 2007
The Landau-Lifshitz-Gilbert equation describes magnetic behavior in ferromagnetic materials. Construction of numerical strategies to approximate weak solutions for this equation is made difficult by its top order nonlinearity and nonconvex constraint. In this paper, we discuss necessary scaling of numerical parameters and provide a refined convergence result for the scheme first proposed by Alouges and Jaisson (2006). As an application, we numerically study discrete finite time blowup in two dimensions.