Geodesic
Construction of convergent adaptive weighted essentially non-oscillatory schemes for Hamilton-Jacobi equations on triangular meshes
Applications of Mathematics, Tome 66 (2021) no. 4, pp. 599-617

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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 the derivative) instead of weighted essentially non-oscillatory approximations. Through detailed numerical experiments, the convergence and effectiveness of the proposed adaptive schemes are demonstrated.
DOI : 10.21136/AM.2021.0368-19
Classification : 35F21, 65M12, 65M50
Keywords: Hamilton-Jacobi equation; first order monotone scheme; high order scheme; weighted essentially non-oscillatory scheme; adaptive scheme; convergence 
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Kim, Kwangil; Hong, Unhyok; Ri, Kwanhung; Yu, Juhyon. Construction of convergent adaptive weighted essentially non-oscillatory schemes for Hamilton-Jacobi equations on triangular meshes. Applications of Mathematics, Tome 66 (2021) no. 4, pp. 599-617. doi: 10.21136/AM.2021.0368-19

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