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

Title
A Sixth-Order Weighted Essentially Non-oscillatory Schemes Based on Exponential Polynomials for Hamilton–Jacobi Equations
Authors
Ha Y.Kim C.H.Yang H.Yoon J.
Ewha Authors
윤정호
SCOPUS Author ID
윤정호scopus
Issue Date
2017
Journal Title
Journal of Scientific Computing
ISSN
0885-7474JCR Link
Citation
pp. 1 - 26
Keywords
Approximation orderExponential polynomialsHamilton–Jacobi equationSmoothness indicatorsWENO scheme
Publisher
Springer New York LLC
Indexed
SCIE; SCOPUS scopus
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. © 2017 Springer Science+Business Media, LLC, part of Springer Nature
DOI
10.1007/s10915-017-0603-8
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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