Displaying similar documents to “Convergence of a proposed adaptive WENO scheme for Hamilton-Jacobi equations”

WENO-Z scheme with new nonlinear weights for Hamilton-Jacobi equations and adaptive approximation

Kwangil Kim, Kwanhung Ri, Wonho Han (2025)

Applications of Mathematics

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A new fifth-order weighted essentially nonoscillatory (WENO) scheme is designed to approximate Hamilton-Jacobi equations. As employing a fifth-order linear approximation and three third-order ones on the same six-point stencil as before, a newly considered WENO-Z methodology is adapted to define nonlinear weights and the final WENO reconstruction results in a simple and clear convex combination. The scheme has formal fifth-order accuracy in smooth regions of the solution and nonoscillating...

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

Kwangil Kim, Unhyok Hong, Kwanhung Ri, Juhyon Yu (2021)

Applications of Mathematics

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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...

On the numerical approximation of first-order Hamilton-Jacobi equations

Rémi Abgrall, Vincent Perrier (2007)

International Journal of Applied Mathematics and Computer Science

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Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.

Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group

Yves Achdou, Italo Capuzzo-Dolcetta (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We propose and analyze numerical schemes for viscosity solutions of time-dependent Hamilton-Jacobi equations on the Heisenberg group. The main idea is to construct a grid compatible with the noncommutative group geometry. Under suitable assumptions on the data, the Hamiltonian and the parameters for the discrete first order scheme, we prove that the error between the viscosity solution computed at the grid nodes and the solution of the discrete problem behaves like h where is the mesh...