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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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Exact sequences on Worsey–Farin splits
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by Johnny Guzmán, Anna Lischke and Michael Neilan HTML | PDF
Math. Comp. 91 (2022), 2571-2608 Request permission

Abstract:

We construct several smooth finite element spaces defined on three-dimensional Worsey–Farin splits. In particular, we construct $C^1$, $H^1(\operatorname {curl})$, and $H^1$-conforming finite element spaces and show the discrete spaces satisfy local exactness properties. A feature of the spaces is their low polynomial degree and lack of extrinsic supersmoothness at subsimplices of the mesh. In the lowest order case, the last two spaces in the sequence consist of piecewise linear and piecewise constant spaces, and are suitable for the discretization of the (Navier-)Stokes equation.
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Additional Information
  • Johnny Guzmán
  • Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
  • MR Author ID: 775211
  • Email: johnny_guzman@brown.edu
  • Anna Lischke
  • Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
  • MR Author ID: 1214513
  • Email: anna_lischke@alumni.brown.edu
  • Michael Neilan
  • Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
  • MR Author ID: 824091
  • Email: neilan@pitt.edu
  • Received by editor(s): July 7, 2021
  • Received by editor(s) in revised form: February 1, 2022
  • Published electronically: July 12, 2022
  • Additional Notes: The first author was supported in part by NSF grant DMS–1913083. The third author was supported in part by NSF grant DMS–2011733.
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 2571-2608
  • MSC (2020): Primary 65M60, 65L60, 65N30; Secondary 76M10, 78M10
  • DOI: https://doi.org/10.1090/mcom/3746
  • MathSciNet review: 4473097