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

2021; Springer Science+Business Media; Volume: 66; Issue: 4 Linguagem: Inglês

10.21136/am.2021.0368-19

1572-9109

Kwang-Il Kim, Unhyok Hong, Kwanhung Ri, Juhyon Yu,

Numerical methods for differential equations

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.