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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.


Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence
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by Erik Burman and Alexandre Ern PDF
Math. Comp. 74 (2005), 1637-1652 Request permission


We analyze a nonlinear shock-capturing scheme for $H^1$-conform- ing, piecewise-affine finite element approximations of linear elliptic problems. The meshes are assumed to satisfy two standard conditions: a local quasi-uniformity property and the Xu–Zikatanov condition ensuring that the stiffness matrix associated with the Poisson equation is an $M$-matrix. A discrete maximum principle is rigorously established in any space dimension for convection-diffusion-reaction problems. We prove that the shock-capturing finite element solution converges to that without shock-capturing if the cell Péclet numbers are sufficiently small. Moreover, in the diffusion-dominated regime, the difference between the two finite element solutions super-converges with respect to the actual approximation error. Numerical experiments on test problems with stiff layers confirm the sharpness of the a priori error estimates.
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Additional Information
  • Erik Burman
  • Affiliation: Ecole Polytechnique Federale de Lausanne, Institute of Analysis and Scientific Computing, 1015 Lausanne, Switzerland
  • MR Author ID: 602430
  • Email:
  • Alexandre Ern
  • Affiliation: CERMICS, Ecole nationale des ponts et chaussées, 6 et 8, avenue B. Pascal, 77455 Marne la Vallée cedex 2, France
  • MR Author ID: 349433
  • Email:
  • Received by editor(s): February 18, 2003
  • Received by editor(s) in revised form: August 16, 2004
  • Published electronically: June 7, 2005
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 74 (2005), 1637-1652
  • MSC (2000): Primary 65N12, 65N30, 76R99
  • DOI:
  • MathSciNet review: 2164090