Article ID Journal Published Year Pages File Type
4643174 Journal of Computational and Applied Mathematics 2006 10 Pages PDF
Abstract

In this paper, a TVD-type difference scheme which satisfies maximum principle is developed for 2D scalar Hamilton–Jacobi equations on unstructured triangular meshes. The main ideas are node-based approximations and derivative-limited reconstruction with quadratic interpolation polynomial. The solution's slope satisfies maximum principle. Numerical experiments are performed to demonstrate high-order accuracy in smooth fields and good resolution of derivative singularities. The new method is simpler than WENO.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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