<div class="csl-bib-body">
<div class="csl-entry">Akrivis, G., Feischl, M., Kovács, B., & Lubich, C. (2021). HIGHER-ORDER LINEARLY IMPLICIT FULL DISCRETIZATION OF THE LANDAU–LIFSHITZ–GILBERT EQUATION. <i>Mathematics of Computation</i>, <i>90</i>(329), 995–1038. https://doi.org/10.1090/mcom/3597</div>
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dc.identifier.issn
0025-5718
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/168394
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dc.description.abstract
For the Landau-Lifshitz-Gilbert (LLG) equation of micromagnetics we study linearly implicit backward difference formula (BDF) time discretizations up to order 5 combined with higher-order non-conforming finite element space discretizations, which are based on the weak formulation due to Alouges but use approximate tangent spaces that are defined by L2-averaged instead of nodal orthogonality constraints. We prove stability and optimalorder error bounds in the situation of a sufficiently regular solution. For the BDF methods of orders 3 to 5, this requires that the damping parameter in the LLG equations be above a positive threshold; this condition is not needed for the A-stable methods of orders 1 and 2, for which furthermore a discrete energy inequality irrespective of solution regularity is proved.
en
dc.language.iso
en
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dc.publisher
AMER MATHEMATICAL SOC
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dc.relation.ispartof
Mathematics of Computation
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dc.subject
BDF methods
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dc.subject
energy technique
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dc.subject
Landau— Lifshitz-Gilbert equation
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dc.subject
non-conforming finite element method
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dc.subject
stability
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dc.title
HIGHER-ORDER LINEARLY IMPLICIT FULL DISCRETIZATION OF THE LANDAU–LIFSHITZ–GILBERT EQUATION