A Sixth-Order Weighted Essentially Non-oscillatory Schemes Based on Exponential Polynomials for Hamilton-Jacobi Equations
- 주제(키워드) WENO scheme , Exponential polynomials , Smoothness indicators , Approximation order , Hamilton-Jacobi equation
- 주제(기타) Mathematics, Applied
- 설명문(일반) [Ha, Youngsoo] Seoul Natl Univ, Dept Math, Seoul, South Korea; [Kim, Chang Ho] Konkuk Univ, Dept Comp Engn, Glocal Campus, Chungju 380701, South Korea; [Yang, Hyoseon; Yoon, Jungho] Ewha W Univ, Dept Math, Seoul 120750, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 SPRINGER/PLENUM PUBLISHERS
- 발행년도 2018
- URI http://www.dcollection.net/handler/ewha/000000151522
- 본문언어 영어
- Published As http://dx.doi.org/10.1007/s10915-017-0603-8
초록/요약
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.
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