Stable C^1-conforming finite element methods for the Landau–Lifshitz–Baryakhtar equation
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The Landau–Lifshitz–Baryakhtar equation describes the evolution of magnetic spin field in magnetic materials at elevated temperature below the Curie temperature, when long-range interactions and longitudinal dynamics are taken into account. We propose two linear fully-discrete C^1-conforming methods to solve the problem, namely a semi-implicit Euler method and a semi-implicit BDF method, and show that these schemes are unconditionally stable. Error analysis is performed which shows optimal convergence rates in each case. Numerical results corroborate our theoretical results.
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