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A Locally Conservative High-Order Least-Squares Formulation in Curvilinear Coordinates

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 106))

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Abstract

We present a locally conservative spectral least-squares formulation for the scalar diffusion-reaction equation in curvilinear coordinates. Careful selection of a least squares functional and compatible finite dimensional subspaces for the solution space yields the conservation properties. Numerical examples confirm the theoretical properties of the method.

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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Acknowledgements

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR).

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Authors and Affiliations

  1. TU Delft, Kluyverweg 1, 2629 HS, Delft, The Netherlands

    Marc Gerritsma

  2. Computational Mathematics, Sandia National Laboratories, Mail Stop 1320, Albuquerque, NM, 87185, USA

    Pavel Bochev

Authors
  1. Marc Gerritsma
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  2. Pavel Bochev
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Corresponding author

Correspondence to Marc Gerritsma .

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Editors and Affiliations

  1. School of Computing , University of Utah, Salt Lake City, Utah, USA

    Robert M. Kirby

  2. School of Computing, University of Utah, Salt Lake City, Utah, USA

    Martin Berzins

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

    Jan S. Hesthaven

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Gerritsma, M., Bochev, P. (2015). A Locally Conservative High-Order Least-Squares Formulation in Curvilinear Coordinates. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_19

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