Error estimates for a semi-implicit numerical scheme solving the Landau–Lifshitz equation with an exchange field
Ivan Cimrák · IMA Journal of Numerical Analysis · 2005
We study the Landau–Lifshitz (LL) equation describing the evolution of spin fields in continuum ferromagnets. We consider the 3D case when the effective field arising in the LL equation includes exchange interaction, the most challenging case. This setting corresponds to the pure isotropic case without a demagnetizing field. We derive some regularity results for the exact solution to the LL with Neumann-type boundary conditions. We modify the numerical scheme studied by A. Prohl in two dimensions and we prove error estimates for this scheme in three dimensions.