Padé-Legendre Interpolants for Gibbs Reconstruction

Authors:
J. S. Hesthaven;S. M. Kaber;L. Lurati
Affiliations:
Division of Applied Mathematics, Brown University, Providence, USA 02912;Laboratoire Jacques-Louis Lions, Université Pierre & Marie Curie, Paris cedex 05, France 75252;Division of Applied Mathematics, Brown University, Providence, USA 02912
Venue:
Journal of Scientific Computing
Year:
2006

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Abstract

We discuss the use of Padé-Legendre interpolants as an approach for the postprocessing of data contaminated by Gibbs oscillations. A fast interpolation based reconstruction is proposed and its excellent performance illustrated on several problems. Almost non-oscillatory behavior is shown without knowledge of the position of discontinuities. Then we consider the performance for computational data obtained from nontrivial tests, revealing some sensitivity to noisy data. A domain decomposition approach is proposed as a partial resolution to this and illustrated with examples.