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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.

 

Analysis of local discontinuous Galerkin methods with generalized numerical fluxes for linearized KdV equations
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by Jia Li, Dazhi Zhang, Xiong Meng and Boying Wu HTML | PDF
Math. Comp. 89 (2020), 2085-2111 Request permission

Abstract:

In this paper, we consider the local discontinuous Galerkin (LDG) method using generalized numerical fluxes for linearized Korteweg–de Vries equations. In particular, since the dispersion term dominates, we are able to choose a downwind-biased flux in possession of the anti-dissipation property for the convection term to compensate the numerical dissipation of the dispersion term. This is beneficial to obtain a lower growth of the error and to accurately capture the exact solution without phase errors for long time simulations, when compared with traditional upwind and alternating fluxes. By establishing relations of three different numerical viscosity coefficients, we first show a uniform stability for the auxiliary variables and the prime variable as well as its time derivative. Moreover, the numerical initial condition is suitably chosen, which is the LDG approximation with the same fluxes to a steady–state equation. Finally, optimal error estimates are obtained by virtue of generalized Gauss–Radau projections. Numerical experiments are given to verify the theoretical results.
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Additional Information
  • Jia Li
  • Affiliation: School of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People’s Republic of China
  • Email: jli@hit.edu.cn
  • Dazhi Zhang
  • Affiliation: School of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People’s Republic of China
  • MR Author ID: 891440
  • Email: zhangdazhi@hit.edu.cn
  • Xiong Meng
  • Affiliation: School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People’s Republic of China
  • MR Author ID: 998988
  • Email: xiongmeng@hit.edu.cn
  • Boying Wu
  • Affiliation: School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People’s Repbulic of China
  • MR Author ID: 261930
  • Email: mathwby@hit.edu.cn
  • Received by editor(s): October 5, 2018
  • Received by editor(s) in revised form: November 3, 2019
  • Published electronically: May 5, 2020
  • Additional Notes: The research of the first author was supported by NSFC grants 11971132 and 11501149.
    The research of the second author was supported by National Key Research and Development Program of China with grant number 2017YFB1401801.
    The research of the third author was supported by NSFC grants 11971132 and 11501149.
    The third author is the corresponding author.
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 89 (2020), 2085-2111
  • MSC (2010): Primary 65M12, 65M15, 65M60
  • DOI: https://doi.org/10.1090/mcom/3550
  • MathSciNet review: 4109561