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Bryson, Steve; Levy, Doron

Mapped WENO and weighted power ENO reconstructions in semi-discrete central schemes for Hamilton-Jacobi equations. (English) Zbl 1096.65081

Appl. Numer. Math. 56, No. 9, 1211-1224 (2006).
Summary: We incorporate new high-order weighted essentially nonoscillatory (WENO)-type reconstructions into Godunov-type central schemes for Hamilton-Jacobi equations. We study schemes that are obtained by combining the Kurganov-Noelle-Petrova flux with the weighted power ENO and the mapped WENO reconstructions. We also derive new variants of these reconstructions by composing the weighted power ENO and the mapped WENO reconstructions with each other. While all schemes are, formally, fifth-order accurate, we show that the quality of the approximation does depend on the particular reconstruction that is being used. In certain cases, it is shown that the approximate solution may not converge to the viscosity solution at all.

Cited in 25 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games

Keywords:

Hamilton-Jacobi equations; semi-discrete schemes; numerical examples; weighted essentially non-oscillatory-type reconstructions; Godunov-type central schemes; Kurganov-Noelle-Petrova flux; viscosity solution
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References:

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