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Value iteration convergence of $\epsilon$-monotone schemes for stationary Hamilton-Jacobi equations

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  • We present an abstract convergence result for the fixed point approximation of stationary Hamilton--Jacobi equations. The basic assumptions on the discrete operator are invariance with respect to the addition of constants, $\epsilon$-monotonicity and consistency. The result can be applied to various high-order approximation schemes which are illustrated in the paper. Several applications to Hamilton--Jacobi equations and numerical tests are presented.
    Mathematics Subject Classification: Primary: 65M12, 49L25; Secondary: 65M06, 65M08.

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