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Fifth-Order Weighted Power-ENO Schemes for Hamilton-Jacobi Equations

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Abstract

We design a class of Weighted Power-ENO (Essentially Non-Oscillatory) schemes to approximate the viscosity solutions of Hamilton-Jacobi (HJ) equations. The essential idea of the Power-ENO scheme is to use a class of extended limiters to replace the minmod type limiters in the classical third-order ENO schemes so as to improve resolution near kinks where the solution has discontinuous gradients. Then a weighting strategy based on appropriate smoothness indicators lifts the scheme to be fifth-order accurate. In particular, numerical examples indicate that the Weighted Power_{3ENO5 works for general HJ equations while the Weighted Power_{\inftyENO5 works for non-linear convex HJ equations. Numerical experiments also demonstrate the accuracy and the robustness of the new schemes

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Authors and Affiliations

  1. Departamento de Matematica Aplicada, University of Valencia, Valencia, Spain

    Susana Serna

  2. Department of Mathematics, UCLA, Los Angeles, CA, 90095-1555, USA

    Jianliang Qian

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  1. Susana Serna
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  2. Jianliang Qian
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Correspondence to Susana Serna.

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Serna, S., Qian, J. Fifth-Order Weighted Power-ENO Schemes for Hamilton-Jacobi Equations. J Sci Comput 29, 57–81 (2006). https://doi.org/10.1007/s10915-005-9015-2

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  • DOI: https://doi.org/10.1007/s10915-005-9015-2

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