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A third-order WENO scheme based on exponential polynomials for Hamilton-Jacobi equations

Title
A third-order WENO scheme based on exponential polynomials for Hamilton-Jacobi equations
Authors
Kim C.H.Ha Y.Yang H.Yoon J.
Ewha Authors
윤정호
SCOPUS Author ID
윤정호scopus
Issue Date
2021
Journal Title
Applied Numerical Mathematics
ISSN
0168-9274JCR Link
Citation
Applied Numerical Mathematics vol. 165, pp. 167 - 183
Keywords
Approximation orderExponential polynomialsExponential vanishing momentHamilton-Jacobi equationSmoothness indicatorsWENO scheme
Publisher
Elsevier B.V.
Indexed
SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
In this study, we provide a novel third-order weighted essentially non-oscillatory (WENO) method to solve Hamilton-Jacobi equations. The key idea is to incorporate exponential polynomials to construct numerical fluxes and smoothness indicators. First, the new smoothness indicators are designed by using the finite difference operator annihilating exponential polynomials such that singular regions can be distinguished from smooth regions more efficiently. Moreover, to construct numerical flux, we employ an interpolation method based on exponential polynomials which yields improved results around steep gradients. The proposed scheme retains the optimal order of accuracy (i.e., three) in smooth areas, even near the critical points. To illustrate the ability of the new scheme, some numerical results are provided along with comparisons with other WENO schemes. © 2021 IMACS
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DOI
10.1016/j.apnum.2021.01.020
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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