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Hermite WENO schemes for Hamilton-Jacobi equations. (English) Zbl 1070.65078

Summary: A class of weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving Hamilton-Jacobi equations is presented. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and used in the reconstruction, while only the function values are evolved and used in the original WENO schemes. Comparing with the original WENO schemes of G.-S. Jiang and D. Peng [SIAM J. Sci. Comput. 21, No. 6, 2126–2143 (2000; Zbl 0957.35014)] for Hamilton-Jacobi equations, one major advantage of HWENO schemes is its compactness in the reconstruction. Extensive numerical experiments are performed to illustrate the capability of the method.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations

Citations:

Zbl 0957.35014
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Full Text: DOI

References:

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