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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.

 

Positivity preserving finite element approximation
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by Ricardo H. Nochetto and Lars B. Wahlbin PDF
Math. Comp. 71 (2002), 1405-1419 Request permission

Abstract:

We consider finite element operators defined on “rough” functions in a bounded polyhedron $\Omega$ in $\mathbb {R}^N$. Insisting on preserving positivity in the approximations, we discover an intriguing and basic difference between approximating functions which vanish on the boundary of $\Omega$ and approximating general functions which do not. We give impossibility results for approximation of general functions to more than first order accuracy at extreme points of $\Omega$. We also give impossibility results about invariance of positive operators on finite element functions. This is in striking contrast to the well-studied case without positivity.
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Additional Information
  • Ricardo H. Nochetto
  • Affiliation: Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
  • MR Author ID: 131850
  • Email: rhn@math.umd.edu
  • Lars B. Wahlbin
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
  • Email: wahlbin@math.cornell.edu
  • Received by editor(s): November 5, 1999
  • Received by editor(s) in revised form: November 21, 2000
  • Published electronically: November 20, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Math. Comp. 71 (2002), 1405-1419
  • MSC (2000): Primary 41A25, 41A36, 65D05, 65N15, 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-01-01369-2
  • MathSciNet review: 1933037