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- W2124772009 abstract "We present the first fifth-order, semi-discrete central-upwind method for approximating solutions of multi-dimensional Hamilton–Jacobi equations. Unlike most of the commonly used high-order upwind schemes, our scheme is formulated as a Godunov-type scheme. The scheme is based on the fluxes of Kurganov–Tadmor and Kurganov–Noelle–Petrova, and is derived for an arbitrary number of space dimensions. A theorem establishing the monotonicity of these fluxes is provided. The spatial discretization is based on a weighted essentially non-oscillatory reconstruction of the derivative. The accuracy and stability properties of our scheme are demonstrated in a variety of examples. A comparison between our method and other fifth-order schemes for Hamilton–Jacobi equations shows that our method exhibits smaller errors without any increase in the complexity of the computations." @default.
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- W2124772009 date "2003-07-01" @default.
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- W2124772009 title "High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton–Jacobi equations" @default.
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- W2124772009 doi "https://doi.org/10.1016/s0021-9991(03)00201-8" @default.
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