Convergence of a non-monotone scheme for Hamilton¨CJacobi¨CBellman equations with discontinous initial data

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• 作者：Olivier Bokanowski ; Nadia Megdich and Hasnaa Zidani
• 关键词：Mathematics Subject Classification (2000) 65M12 ; 65M15 ; 35F25 ; 35F99 ; 49L25
• 刊名：Numerische Mathematik
• 出版年：2010
• 出版时间：March, 2010
• 年：2010
• 卷：115
• 期：1
• 页码：1-44
• 全文大小：826.7 KB

文摘

We prove the convergence of a non-monotonous scheme for a one-dimensional first order Hamilton–Jacobi–Bellman equation of the form v _t + max _α (f(x, α)v _x ) = 0, v(0, x) = v ₀(x). The scheme is related to the HJB-UltraBee scheme suggested in Bokanowski and Zidani (J Sci Comput 30(1):1–33, 2007). We show for general discontinuous initial data a first-order convergence of the scheme, in L 1-norm, towards the viscosity solution. We also illustrate the non-diffusive behavior of the scheme on several numerical examples.