A third-order WENO scheme based on exponential polynomials for Hamilton-Jacobi equations
- 주제(키워드) Approximation order , Exponential polynomials , Exponential vanishing moment , Hamilton-Jacobi equation , Smoothness indicators , WENO scheme
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Elsevier B.V.
- 발행년도 2021
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000181673
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.apnum.2021.01.020
초록/요약
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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