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An Adaptive Variable Order Quadrature Strategy

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 119))

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Abstract

We propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this way we aim to account for local smoothness properties of the integrand as effectively as possible, and thereby achieve highly accurate results in a very efficient manner. Indeed, this idea originates from so-called hp-version finite element methods which are known to deliver high-order convergence rates, even for nonsmooth functions.

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Acknowledgements

Thomas P. Wihler acknowledges the financial support by the Swiss National Science Foundation (SNF).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

    Paul Houston

  2. Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland

    Thomas P. Wihler

Authors
  1. Paul Houston
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  2. Thomas P. Wihler
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Corresponding author

Correspondence to Paul Houston .

Editor information

Editors and Affiliations

  1. School of Mechanical Engineering, University of Campinas, Campinas, Brazil

    Marco L. Bittencourt

  2. Department of Civil Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

    Ney A. Dumont

  3. EPFL-SB-MATHICSE-MCSS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Jan S. Hesthaven

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Houston, P., Wihler, T.P. (2017). An Adaptive Variable Order Quadrature Strategy. In: Bittencourt, M., Dumont, N., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Lecture Notes in Computational Science and Engineering, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-65870-4_38

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