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ENO Reconstruction and ENO Interpolation Are Stable

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Abstract

We prove that the ENO reconstruction and ENO interpolation procedures are stable in the sense that the jump of the reconstructed ENO point values at each cell interface has the same sign as the jump of the underlying cell averages across that interface. Moreover, we prove that the size of these jumps after reconstruction relative to the jump of the underlying cell averages is bounded. Similar sign properties and the boundedness of the jumps hold for the ENO interpolation procedure. These estimates, which are shown to hold for ENO reconstruction and interpolation of arbitrary order of accuracy and on nonuniform meshes, indicate a remarkable rigidity of the piecewise polynomial ENO procedure.

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Acknowledgements

S.M. thanks Prof. Mike Floater of CMA, Oslo for useful discussions. The research of E.T. was supported by grants from the National Science Foundation, DMS#10-08397, and the Office of Naval Research, ONR#N000140910385 and #000141210318.

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Authors and Affiliations

  1. Seminar for Applied Mathematics, ETH Zürich, HG J 48, Rämistrasse 101, Zürich, Switzerland

    Ulrik S. Fjordholm & Siddhartha Mishra

  2. Department of Mathematics, Center of Scientific Computation and Mathematical Modeling (CSCAMM), Institute for Physical Sciences and Technology (IPST), University of Maryland, College Park, MD, 20742-4015, USA

    Eitan Tadmor

Authors
  1. Ulrik S. Fjordholm
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  2. Siddhartha Mishra
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  3. Eitan Tadmor
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Correspondence to Eitan Tadmor.

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Communicated by Nira Dyn.

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Fjordholm, U.S., Mishra, S. & Tadmor, E. ENO Reconstruction and ENO Interpolation Are Stable. Found Comput Math 13, 139–159 (2013). https://doi.org/10.1007/s10208-012-9117-9

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  • DOI: https://doi.org/10.1007/s10208-012-9117-9

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