98-32   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Andreas Prohl:

Error analysis for the computation of microstructure in cubic ferromagnets

It is observed in cubic ferromagnetic materials that domains of different size and magnetic orientation appear, with the structure of it also depending on the shape of the domain. Magnetizations can be mathematically modelized by minima of a nonconvex function. -- Finite element discretizations introduce a numerical scaling of the spatial discretization to the model and its minimizers --- that often cannot capture the wide range scaling of magnetizations that solve the continuous model, like e.g. refined structures close to the boundary of the ferromagnet that can be observed in experiments. This is one main reason for suboptimal convergence rates that will be verified in the present paper. Hence, graduate meshes that are combined with an adaptive grid-refinement strategy are introduced to the problem in a second step to allow for the resolution of refined microstructure near the boundary in the minimization process, leading to improved convergence statements.

Keywords: finite element method, non-convex minimization, microstructure, multiscale, micromagnetism.


Mail an Jens Burmeister
[Thu Feb 19 18:56:34 2009]
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