Geodesic
Convergence of a proposed adaptive WENO scheme for Hamilton-Jacobi equations
Applications of Mathematics, Tome 68 (2023) no. 5, pp. 661-684

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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 nonconvex ones, the convergence and effectiveness of the adaptive WENO scheme are demonstrated.
DOI : 10.21136/AM.2023.0264-22
Classification : 35F21, 65M06, 65M12
Keywords: Hamilton-Jacobi equations; WENO scheme; adaptive WENO scheme; nonconvex Hamiltonian; convergence 
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Han, Wonho; Kim, Kwangil; Hong, Unhyok. Convergence of a proposed adaptive WENO scheme for Hamilton-Jacobi equations. Applications of Mathematics, Tome 68 (2023) no. 5, pp. 661-684. doi: 10.21136/AM.2023.0264-22

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