TY - JOUR
T1 - A third-order WENO scheme based on exponential polynomials for Hamilton-Jacobi equations
AU - Kim, Chang Ho
AU - Ha, Youngsoo
AU - Yang, Hyoseon
AU - Yoon, Jungho
N1 - Funding Information:
J. Yoon was supported by the National Research Foundation of Korea (NRF) under the grant NRF-2015R1A5A1009350 and NRF-2020R1A2C1A01005894 .
Publisher Copyright:
© 2021 IMACS
PY - 2021/7
Y1 - 2021/7
N2 - 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.
AB - 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.
KW - Approximation order
KW - Exponential polynomials
KW - Exponential vanishing moment
KW - Hamilton-Jacobi equation
KW - Smoothness indicators
KW - WENO scheme
UR - http://www.scopus.com/inward/record.url?scp=85101211062&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2021.01.020
DO - 10.1016/j.apnum.2021.01.020
M3 - Article
AN - SCOPUS:85101211062
SN - 0168-9274
VL - 165
SP - 167
EP - 183
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -