A Sixth-Order Weighted Essentially Non-oscillatory Schemes Based on Exponential Polynomials for Hamilton–Jacobi Equations

Youngsoo Ha, Chang Ho Kim, Hyoseon Yang, Jungho Yoon

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8 Scopus citations

Abstract

In this study, we present a new sixth-order finite difference weighted essentially non-oscillatory (WENO) scheme for solving Hamilton–Jacobi equations. The proposed scheme recovers the maximal approximation order in smooth regions without loss of accuracy at critical points. We incorporate exponential polynomials into the scheme to obtain better approximation near steep gradients without spurious oscillations. In order to design nonlinear weights based on exponential polynomials, we suggest an alternative approach to construct Lagrange-type exponential functions reproducing the cell-average values of exponential basis functions. Using the Lagrange-type exponential functions, we provide a detailed analysis of the approximation order of the proposed WENO scheme. Compared to other WENO schemes, the proposed scheme is simpler to implement, yielding better approximations with lower computational costs. A number of numerical experiments are presented to demonstrate the performance of the proposed scheme.

Original languageEnglish
Pages (from-to)1675-1700
Number of pages26
JournalJournal of Scientific Computing
Volume75
Issue number3
DOIs
StatePublished - 1 Jun 2018

Keywords

  • Approximation order
  • Exponential polynomials
  • Hamilton–Jacobi equation
  • Smoothness indicators
  • WENO scheme

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