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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.


Failure of the discrete maximum principle for an elliptic finite element problem
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by Andrei Drăgănescu, Todd F. Dupont and L. Ridgway Scott PDF
Math. Comp. 74 (2005), 1-23 Request permission


There has been a long-standing question of whether certain mesh restrictions are required for a maximum condition to hold for the discrete equations arising from a finite element approximation of an elliptic problem. This is related to knowing whether the discrete Green’s function is positive for triangular meshes allowing sufficiently good approximation of $H^1$ functions. We study this question for the Poisson problem in two dimensions discretized via the Galerkin method with continuous piecewise linears. We give examples which show that in general the answer is negative, and furthermore we extend the number of cases where it is known to be positive. Our techniques utilize some new results about discrete Green’s functions that are of independent interest.
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Additional Information
  • Andrei Drăgănescu
  • Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
  • Email:
  • Todd F. Dupont
  • Affiliation: Department of Computer Science, University of Chicago, Chicago, Illinois 60637
  • Email:
  • L. Ridgway Scott
  • Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
  • MR Author ID: 157720
  • Email:
  • Received by editor(s): May 12, 2003
  • Received by editor(s) in revised form: June 8, 2003
  • Published electronically: March 23, 2004
  • Additional Notes: The work of the authors was supported by the ASCI Flash Center at the University of Chicago under DOE contract B532820 and by the MRSEC Program of the National Science Foundation under award DMR-0213745
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1-23
  • MSC (2000): Primary 65N30; Secondary 65N50
  • DOI:
  • MathSciNet review: 2085400