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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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