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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.


Superconvergent discontinuous Galerkin methods for second-order elliptic problems
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by Bernardo Cockburn, Johnny Guzmán and Haiying Wang PDF
Math. Comp. 78 (2009), 1-24 Request permission


We identify discontinuous Galerkin methods for second-order elliptic problems in several space dimensions having superconvergence properties similar to those of the Raviart-Thomas and the Brezzi-Douglas-Marini mixed methods. These methods use polynomials of degree $k\ge 0$ for both the potential as well as the flux. We show that the approximate flux converges in $L^2$ with the optimal order of $k+1$, and that the approximate potential and its numerical trace superconverge, in $L^2$-like norms, to suitably chosen projections of the potential, with order $k+2$. We also apply element-by-element postprocessing of the approximate solution to obtain new approximations of the flux and the potential. The new approximate flux is proven to have normal components continuous across inter-element boundaries, to converge in $L^2$ with order $k+1$, and to have a divergence converging in $L^2$ also with order $k+1$. The new approximate potential is proven to converge with order $k+2$ in $L^2$. Numerical experiments validating these theoretical results are presented.
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Additional Information
  • Bernardo Cockburn
  • Affiliation: School of Mathematics, University of Minnesota, Vincent Hall, Minneapolis, Minnesota 55455
  • Email:
  • Johnny Guzmán
  • Affiliation: School of Mathematics, University of Minnesota, Vincent Hall, Minneapolis, Minnesota 55455
  • MR Author ID: 775211
  • Email:
  • Haiying Wang
  • Affiliation: Reservoir Engineering Research Institute, 385 Sherman Avenue, Suite 5, Palo Alto, California 94306
  • Email:
  • Received by editor(s): October 9, 2007
  • Received by editor(s) in revised form: January 31, 2008
  • Published electronically: May 19, 2008
  • Additional Notes: B. Cockburn was supported in part by the National Science Foundation (Grant DMS-0712955) and by the University of Minnesota Supercomputing Institute
    J. Guzmán was supported by a National Science Foundation Mathematical Science Postdoctoral Research Fellowship (DMS-0503050)
  • © Copyright 2008 American Mathematical Society
  • Journal: Math. Comp. 78 (2009), 1-24
  • MSC (2000): Primary 65M60, 65N30, 35L65
  • DOI:
  • MathSciNet review: 2448694