Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation

摘要

The Landau-Lifshitz-Gilbert equation describes the dynamics of ferromagnetism, where strong nonlinearity and nonconvexity are hard to tackle: so far, existing explicit schemes to approximate weak solutions suffer from severe time-step restrictions. In this paper, we propose an implicit fully discrete scheme and verify unconditional convergence.