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Polynomial Preserving Recovery for High Frequency Wave Propagation

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Abstract

Polynomial preserving recovery (PPR) was first proposed and analyzed in Zhang and Naga in SIAM J Sci Comput 26(4):1192–1213, (2005), with intensive following applications on elliptic problems. In this paper, we generalize the study of PPR to high-frequency wave propagation. Specifically, we establish the supercloseness between finite element solution and its interpolation with explicit dependence on the frequency of wavefield, and then prove the superconvergence of PPR for high-frequency solutions to wave equation based on the supercloseness. We also present several numerical examples of PPR for both low-frequency and high-frequency wave propagation in order to confirm the theoretical results of superconvergence analysis.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA

    Hailong Guo & Xu Yang

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  1. Hailong Guo
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  2. Xu Yang
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Correspondence to Hailong Guo.

Additional information

This work was partially supported by the NSF Grants DMS-1418936 and DMS-1107291, and Hellman Family Foundation Faculty Fellowship, UC Santa Barbara. We also acknowledge support from the Center for Scientific Computing from the CNSI, MRL: an NSF MRSEC (DMR-1121053) and NSF CNS-0960316.

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Guo, H., Yang, X. Polynomial Preserving Recovery for High Frequency Wave Propagation. J Sci Comput 71, 594–614 (2017). https://doi.org/10.1007/s10915-016-0312-8

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  • DOI: https://doi.org/10.1007/s10915-016-0312-8

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