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The Geometric Basis of Numerical Methods

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Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 95))

Abstract

The relation between physics, its description in terms of partial differential equations and geometry is explored in this paper. Geometry determines the correct weak formulation in finite element methods and also dictates which basis functions should be employed to obtain discrete well-posedness.

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Acknowledgements

The authors want to thank the reviewers for their critical remarks and useful suggestions.

Author information

Authors and Affiliations

  1. Aerospace Engineering, TU Delft, Delft, The Netherlands

    Marc Gerritsma, Artur Palha & Pedro Rebelo

  2. EPFL, Lausanne, Switzerland

    Deepesh Toshniwal

  3. ICES, University of Austin, Austin, TX, USA

    René Hiemstra

  4. Shell Global Solution, Amsterdam, The Netherlands

    Jasper Kreeft

Authors
  1. Marc Gerritsma
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  2. René Hiemstra
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  3. Jasper Kreeft
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  4. Artur Palha
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  5. Pedro Rebelo
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  6. Deepesh Toshniwal
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Corresponding author

Correspondence to Marc Gerritsma .

Editor information

Editors and Affiliations

  1. Institut Polytechnique de Bordeaux, Université de Bordeaux, Pessac, France

    Mejdi Azaïez

  2. Ecole Nationale d'Ingénieurs de Tunis, Université de Tunis El Manar, Tunis, Tunisia

    Henda El Fekih

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

    Jan S. Hesthaven

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Gerritsma, M., Hiemstra, R., Kreeft, J., Palha, A., Rebelo, P., Toshniwal, D. (2014). The Geometric Basis of Numerical Methods. In: Azaïez, M., El Fekih, H., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012. Lecture Notes in Computational Science and Engineering, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-01601-6_2

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