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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...

Construction of convergent adaptive weighted essentially non-oscillatory schemes for Hamilton-Jacobi equations on triangular meshes

Kwangil Kim;  Unhyok Hong;  Kwanhung Ri;  Juhyon Yu — 2021

Applications of Mathematics

We propose a method of constructing convergent high order schemes for Hamilton-Jacobi equations on triangular meshes, which is based on combining a high order scheme with a first order monotone scheme. According to this methodology, we construct adaptive schemes of weighted essentially non-oscillatory type on triangular meshes for nonconvex Hamilton-Jacobi equations in which the first order monotone approximations are occasionally applied near singular points of the solution (discontinuities of...

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