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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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Optimally accurate higher-order finite element methods for polytopial approximations of domains with smooth boundaries
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by James Cheung, Mauro Perego, Pavel Bochev and Max Gunzburger HTML | PDF
Math. Comp. 88 (2019), 2187-2219 Request permission


Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on such meshes. On the other hand, the simplicity of affine meshes makes them a desirable modeling tool in many applications. In this paper, we develop and analyze higher-order accurate finite element methods that remain stable and optimally accurate on polytopial approximations of domains with smooth boundaries. This is achieved by constraining a judiciously chosen extension of the finite element solution on the polytopial domain to weakly match the prescribed boundary condition on the true geometric boundary. We provide numerical examples that highlight key properties of the new method and that illustrate the optimal $H^1$- and $L^2$-norm convergence rates.
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Additional Information
  • James Cheung
  • Affiliation: Interdisciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg, Virginia 24061
  • MR Author ID: 1230885
  • Email:
  • Mauro Perego
  • Affiliation: Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123
  • MR Author ID: 869976
  • Email:
  • Pavel Bochev
  • Affiliation: Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123
  • MR Author ID: 38390
  • Email:
  • Max Gunzburger
  • Affiliation: Department of Scientific Computing, Florida State University, Tallahassee, Florida 32309
  • MR Author ID: 78360
  • Email:
  • Received by editor(s): February 8, 2018
  • Received by editor(s) in revised form: October 28, 2018
  • Published electronically: February 21, 2019
  • Additional Notes: Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.
    This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research. Additionally, the first and fourth authors were supported by US Department of Energy grant DE-SC0009324 and US Air Force Office of Scientific Research grant FA9550-15-1-0001.
  • Journal: Math. Comp. 88 (2019), 2187-2219
  • MSC (2010): Primary 65N30
  • DOI:
  • MathSciNet review: 3957891