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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation
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by Georgios Akrivis, Michael Feischl, Balázs Kovács and Christian Lubich HTML | PDF
Math. Comp. 90 (2021), 995-1038 Request permission


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 $L^2$-averaged instead of nodal orthogonality constraints. We prove stability and optimal-order 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.
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Additional Information
  • Georgios Akrivis
  • Affiliation: Department of Computer Science & Engineering, University of Ioannina, 451 10 Ioannina, Greece; Institute of Applied and Computational Mathematics, FORTH, 700 13 Heraklion, Crete, Greece
  • MR Author ID: 24080
  • Email:
  • Michael Feischl
  • Affiliation: Institute for Analysis and Scientific Computing (E 101), Technical University Wien, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria
  • MR Author ID: 965785
  • Email:
  • Balázs Kovács
  • Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle, D-72076 Tübingen, Germany
  • ORCID: 0000-0001-9872-3474
  • Email:
  • Christian Lubich
  • Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle, D-72076 Tübingen, Germany
  • MR Author ID: 116445
  • Email:
  • Received by editor(s): March 13, 2019
  • Received by editor(s) in revised form: March 14, 2020
  • Published electronically: February 26, 2021
  • Additional Notes: The work of the second, third, and fourth authors were supported by Deutsche Forschungsgemeinschaft – Project-ID 258734477 – SFB 1173.
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 995-1038
  • MSC (2020): Primary 65M12, 65M15; Secondary 65L06
  • DOI:
  • MathSciNet review: 4232216