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Approximation classes for adaptive higher order finite element approximation

Authors: Fernando D. Gaspoz and Pedro Morin
Journal: Math. Comp. 83 (2014), 2127-2160
MSC (2010): Primary 41A25, 65D05; Secondary 65N30, 65N50
Published electronically: December 17, 2013
MathSciNet review: 3223327
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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

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

Keywords: Adaptive finite elements, Besov spaces, convergence rates, approximation classes
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).
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.