Approximation Schemes for Monotone Systems of Nonlinear Second Order Partial Differential Equations: Convergence Result and Error Estimate

Ariela Briani 1, 2 Fabio Camilli 3 Hasnaa Zidani 1, 4
4 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CNRS - Centre National de la Recherche Scientifique : UMR7641, X - École polytechnique, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : We consider approximation schemes for monotone systems of fully nonlinear second order partial di erential equations. We rst prove a general convergence result for monotone, consistent and regular schemes. This result is a generalization to the well known framework of Barles-Souganidis, in the case of scalar nonlinear equation. Our second main result provides the convergence rate of approximation schemes for weakly coupled systems of Hamilton-Jacobi-Bellman equations. Examples including nite di erence schemes and Semi-Lagrangian schemes are discussed.
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Differential Equations and Applications, Ele-Math, 2012, 4, pp.297-317. 〈10.7153/dea-04-18〉
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Ariela Briani, Fabio Camilli, Hasnaa Zidani. Approximation Schemes for Monotone Systems of Nonlinear Second Order Partial Differential Equations: Convergence Result and Error Estimate. Differential Equations and Applications, Ele-Math, 2012, 4, pp.297-317. 〈10.7153/dea-04-18〉. 〈inria-00627520〉

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