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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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Approximation classes for adaptive higher order finite element approximation
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by Fernando D. Gaspoz and Pedro Morin PDF
Math. Comp. 83 (2014), 2127-2160 Request permission

Abstract:

We provide an almost characterization of the approximation classes appearing when using adaptive finite elements of Lagrange type of any fixed polynomial degree. The characterization is stated in terms of Besov regularity, and requires the approximation within spaces with integrability indices below one. This article generalizes to higher order finite elements the results presented for linear finite elements by Binev et. al.
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Additional Information
  • Fernando D. Gaspoz
  • Affiliation: Institut für Angewandte Mathematik und Numerische Simulation, Universität Stuttgart. Pfaffenwaldring 57, D-70569 Stuttgart, Germany
  • MR Author ID: 884857
  • Email: fernando.gaspoz@ians.uni-stuttgart.de
  • Pedro Morin
  • Affiliation: Departamento de Matemática, Facultad de Ingeniería Química and Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral and Consejo Nacional de Investigaciones Científicas y Técnicas. IMAL, Güemes 3450, S3000GLN Santa Fe, Argentina
  • Email: pmorin@santafe-conicet.gov.ar
  • Received by editor(s): February 9, 2011
  • Received by editor(s) in revised form: June 13, 2012, November 27, 2012, and December 18, 2012
  • Published electronically: December 17, 2013
  • Additional Notes: The first author was partially supported by DFG through grant SI-814/4-1
    The second author was partially supported by CONICET through grant PIP 112-200801-02182, Universidad Nacional del Litoral through grants CAI+D 062-312, 062-309, and Agencia Nacional de Promoción Científica y Tecnológica, through grant PICT-2008-0622 (Argentina).
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 2127-2160
  • MSC (2010): Primary 41A25, 65D05; Secondary 65N30, 65N50
  • DOI: https://doi.org/10.1090/S0025-5718-2013-02777-9
  • MathSciNet review: 3223327