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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.


Exact smooth piecewise polynomial sequences on Alfeld splits
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by Guosheng Fu, Johnny Guzmán and Michael Neilan HTML | PDF
Math. Comp. 89 (2020), 1059-1091 Request permission


We construct local exact piecewise polynomial sequences on Alfeld splits in any spatial dimension and any polynomial degree. An Alfeld split of a simplex is obtained by connecting the vertices of an $n$-simplex with its barycenter. We show that, on these splits, the kernel of the exterior derivative has enhanced smoothness. Byproducts of this result include characterizations of discrete divergence-free subspaces and simple formulas for the dimensions of smooth polynomial spaces. In addition, we construct analogous global exact sequences and commuting projections in three-dimensions with varying levels of smoothness.
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Additional Information
  • Guosheng Fu
  • Affiliation: Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556
  • MR Author ID: 1061680
  • Email:
  • Johnny Guzmán
  • Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
  • MR Author ID: 775211
  • Email:
  • Michael Neilan
  • Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
  • MR Author ID: 824091
  • Email:
  • Received by editor(s): May 31, 2019
  • Received by editor(s) in revised form: December 10, 2019
  • Published electronically: January 13, 2020
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 89 (2020), 1059-1091
  • MSC (2010): Primary 65N30
  • DOI:
  • MathSciNet review: 4063312