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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.

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Divergence-conforming HDG methods for Stokes flows
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by Bernardo Cockburn and Francisco-Javier Sayas PDF
Math. Comp. 83 (2014), 1571-1598 Request permission


In this paper, we show that by sending the normal stabilization function to infinity in the hybridizable discontinuous Galerkin methods previously proposed in [Comput. Methods Appl. Mech. Engrg. 199 (2010), 582–597], for Stokes flows, a new class of divergence-conforming methods is obtained which maintains the convergence properties of the original methods. Thus, all the components of the approximate solution, which use polynomial spaces of degree $k$, converge with the optimal order of $k+1$ in $L^2$ for any $k \ge 0$. Moreover, the postprocessed velocity approximation is also divergence-conforming, exactly divergence-free and converges with order $k+2$ for $k\ge 1$ and with order $1$ for $k=0$. The novelty of the analysis is that it proceeds by taking the limit when the normal stabilization goes to infinity in the error estimates recently obtained in [Math. Comp., 80 (2011) 723–760].
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Additional Information
  • Bernardo Cockburn
  • Affiliation: School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455
  • Email:
  • Francisco-Javier Sayas
  • Affiliation: Department of Mathematical Sciences, University of Delaware, Ewing Hall, Newark, Delaware 19711
  • MR Author ID: 621885
  • Email:
  • Received by editor(s): July 25, 2011
  • Received by editor(s) in revised form: December 31, 2012
  • Published electronically: March 19, 2014
  • Additional Notes: The first author was partially supported by the National Science Foundation (Grant DMS-0712955) and by the Minnesota Supercomputing Institute.
    The second author was a Visiting Professor of the School of Mathematics, University of Minnesota, during the development of this work, and was partially supported by the National Science Foundation (Grant DMS 1216356).
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 1571-1598
  • MSC (2010): Primary 65M60, 65N30, 35L65
  • DOI:
  • MathSciNet review: 3194122