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The Spectral Element Method Used to Assess the Quality of a Global C 1 Map

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Spectral and High Order Methods for Partial Differential Equations

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 76))

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Abstract

In this work we focus on C 1 maps from a reference domain to a family of deformed domains. The regularity of a map affects the approximation properties of the mapped mesh, and we use the regularity as a measure of the quality of the mesh. To compare the regularities of different maps we consider the convergence of the spectral element method when a Laplace problem is solved on the resulting meshes. C 1

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Acknowledgements

This work has been supported by the Research Council of Norway through a Centre of Excellence grant to the Center for Biomedical Computing.

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Authors and Affiliations

  1. Center for Biomedical Computing, Simula Research Laboratory, 134, 1325, Lysaker, Norway

    A. E. Løvgren

  2. Laboratoire J.-L. Lions, Université Pierre et Marie Curie-Paris6, UMR 7598, Paris, F-75005, France

    Y. Maday

  3. Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI, 02912, USA

    Y. Maday

  4. Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    E. M. Rønquist

Authors
  1. A. E. Løvgren
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  2. Y. Maday
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  3. E. M. Rønquist
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Corresponding author

Correspondence to A. E. Løvgren .

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Editors and Affiliations

  1. , Division of Applied Mathematics, Brown University, George Street 182, Providence, 02912, Rhode Island, USA

    Jan S. Hesthaven

  2. , Department of Mathematical Sciences, Norwegian University of Science and Tech, Trondheim, 7491, Norway

    Einar M. Rønquist

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Løvgren, A.E., Maday, Y., Rønquist, E.M. (2011). The Spectral Element Method Used to Assess the Quality of a Global C 1 Map. In: Hesthaven, J., Rønquist, E. (eds) Spectral and High Order Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 76. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15337-2_42

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