A convergent finite-element-based discretization of the stochastic Landau-Lifshitz-Gilbert equation

Lubomir Banas, Zdzislaw Brzeźniak, Mikhail Neklyudov, Andreas Prohl

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We propose a convergent finite-element-based discretization of the stochastic Landau-Lifshitz-Gilbert equation. The main difficulties in the convergence analysis for this nonlinear stochastic partial differential equation are to properly address the pointwise sphere condition and, in the fully discrete scheme, the Stratonovich noise. Approximations of the scheme proposed here satisfy a sphere constraint at nodal points of the spatial discretization and have finite energies, and their increments may be controlled uniformly with respect to discretization parameters. Sequences of corresponding continuified processes may then be generated which construct weak martingale solutions of the limiting equations.

Original languageEnglish
Pages (from-to)502-549
Number of pages48
JournalIMA Journal of Numerical Analysis
Volume34
Issue number2
Early online date30 Jul 2013
DOIs
Publication statusPublished - 2014

Keywords

  • finite element method
  • stochastic Landau-Lifshitz-Gilbert equation
  • Stratonovich noise
  • time discretization

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

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