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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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Linear finite elements may be only first-order pointwise accurate on anisotropic triangulations
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by Natalia Kopteva PDF
Math. Comp. 83 (2014), 2061-2070 Request permission


We give a counterexample of an anisotropic triangulation on which the exact solution has a second-order error of linear interpolation, while the computed solution obtained using linear finite elements is only first-order pointwise accurate. Our example is given in the context of a singularly perturbed reaction-diffusion equation, whose exact solution exhibits a sharp boundary layer. Furthermore, we give a theoretical justification of the observed numerical phenomena using a finite-difference representation of the considered finite element methods. Both standard and lumped-mass cases are addressed.
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Additional Information
  • Natalia Kopteva
  • Affiliation: Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
  • Address at time of publication: Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow, G1 1XT, United Kingdom
  • MR Author ID: 610720
  • ORCID: 0000-0001-7477-6926
  • Email:
  • Received by editor(s): September 14, 2012
  • Received by editor(s) in revised form: January 22, 2013
  • Published electronically: February 28, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 2061-2070
  • MSC (2010): Primary 65N15, 65N30, 65N50; Secondary 65N06
  • DOI:
  • MathSciNet review: 3223324