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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.


Uniform convergence of the LDG method for a singularly perturbed problem with the exponential boundary layer
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by Huiqing Zhu and Zhimin Zhang PDF
Math. Comp. 83 (2014), 635-663 Request permission


In this paper, we study a uniform convergence property of the local discontinuous Galerkin method (LDG) for a convection-diffusion problem whose solution has exponential boundary layers. A Shishkin mesh is employed. The trail functions in the LDG method are piecewise polynomials that lies in the space $\mathcal {Q}_k$, i.e., are tensor product polynomials of degree at most $k$ in one variable, where $k>0$. We identify that the error of the LDG solution in a DG-norm converges at a rate of $(\ln N/N)^{k+1/2}$; here the total number of mesh points is $O(N^2)$. The numerical experiments show that this rate of convergence is sharp.
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Additional Information
  • Huiqing Zhu
  • Affiliation: Department of Mathematics, The University of Southern Mississippi, Hattiesburg, Mississippi 39406
  • Email:
  • Zhimin Zhang
  • Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202; Beijing Computational Science Research Center, No. 3 Heqing Road, Haidian District, Beijing 100084, China.
  • Email:
  • Received by editor(s): April 2, 2011
  • Received by editor(s) in revised form: June 15, 2012
  • Published electronically: June 25, 2013
  • Additional Notes: Corresponding author: Huiqing Zhu,
    The second author was supported in part by the US National Science Foundation through grant DMS-1115530.
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 635-663
  • MSC (2010): Primary 65N30, 65N12, 65N15
  • DOI:
  • MathSciNet review: 3143687