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Convergence of a proposed adaptive WENO scheme for Hamilton-Jacobi equations

Wonho Han;  Kwangil Kim;  Unhyok Hong — 2023

Applications of Mathematics

We study high-order numerical methods for solving Hamilton-Jacobi equations. Firstly, by introducing new clear concise nonlinear weights and improving their convex combination, we develop WENO schemes of Zhu and Qiu (2017). Secondly, we give an algorithm of constructing a convergent adaptive WENO scheme by applying the simple adaptive step on the proposed WENO scheme, which is based on the introduction of a new singularity indicator. Through detailed numerical experiments on extensive problems including...

WENO-Z scheme with new nonlinear weights for Hamilton-Jacobi equations and adaptive approximation

Kwangil Kim;  Kwanhung Ri;  Wonho Han — 2025

Applications of Mathematics

A new fifth-order weighted essentially nonoscillatory (WENO) scheme is designed to approximate Hamilton-Jacobi equations. As employing a fifth-order linear approximation and three third-order ones on the same six-point stencil as before, a newly considered WENO-Z methodology is adapted to define nonlinear weights and the final WENO reconstruction results in a simple and clear convex combination. The scheme has formal fifth-order accuracy in smooth regions of the solution and nonoscillating behavior...

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