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Keywords:
Hamilton-Jacobi equation; first order monotone scheme; high order scheme; weighted essentially non-oscillatory scheme; adaptive scheme; convergence
Hamilton-Jacobi equation; first order monotone scheme; high order scheme; weighted essentially non-oscillatory scheme; adaptive scheme; convergence
Summary:
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.
References:
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