, Volume 83, Issue 3, pp 427-442

Finite volume schemes for Hamilton–Jacobi equations

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We introduce two classes of monotone finite volume schemes for Hamilton-Jacobi equations. The corresponding approximating functions are piecewise linear defined on a mesh consisting of triangles. The schemes are shown to converge to the viscosity solution of the Hamilton–Jacobi equation.

Received February 25, 1998 / Published online: June 29, 1999