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

Abgrall R., Perrier V.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 3

403-412

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.