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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.


Structure-preserving finite element methods for stationary MHD models
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by Kaibo Hu and Jinchao Xu HTML | PDF
Math. Comp. 88 (2019), 553-581 Request permission


We develop a class of mixed finite element schemes for stationary magnetohydrodynamics (MHD) models, using the magnetic field $\mathbfit {B}$ and the current density $\mathbfit {j}$ as discretization variables. We show that Gauss’s law for the magnetic field, namely $\nabla \cdot \mathbfit {B}=0$, and the energy law for the entire system are exactly preserved in the finite element schemes. Based on some new basic estimates for $H(\mathrm {div})$ finite elements, we show that the new finite element scheme is well-posed. Furthermore, we show the existence of solutions to the nonlinear problems and the convergence of the Picard iterations and the finite element methods under some conditions.
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Additional Information
  • Kaibo Hu
  • Affiliation: Beijing International Center for Mathematical Research, Peking University, Beijing 100871, People’s Republic of China
  • Address at time of publication: Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, Oslo, Norway
  • MR Author ID: 1161425
  • Email:
  • Jinchao Xu
  • Affiliation: Center for Computational Mathematics and Applications and Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
  • MR Author ID: 228866
  • Email:
  • Received by editor(s): March 20, 2015
  • Received by editor(s) in revised form: January 29, 2016, November 13, 2016, September 18, 2017, and November 12, 2017
  • Published electronically: May 29, 2018
  • Additional Notes: This material is based upon work supported in part by the US Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC0014400 and by Beijing International Center for Mathematical Research of Peking University, China.
    The first author was supported in part by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement 339643.
  • © Copyright 2018 American Mathematical Society
  • Journal: Math. Comp. 88 (2019), 553-581
  • MSC (2010): Primary 65N30, 65N12
  • DOI:
  • MathSciNet review: 3882276