Value iteration convergence of "-monotone schemes for stationary Hamilton-Jacobi equations

Abstract : We present an abstract convergence result for the xed point approximation of stationary Hamilton{Jacobi equations. The basic assumptions on the discrete operator are invariance with respect to the addition of constants, "-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.
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Olivier Bokanowski, Maurizio Falcone, Roberto Ferretti, Lars Grüne, Dante Kalise, et al.. Value iteration convergence of "-monotone schemes for stationary Hamilton-Jacobi equations. Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2015, 35 (9), pp.4041 - 4070. ⟨10.3934/dcds.2015.35.4041⟩. ⟨hal-00989495⟩

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