We consider approximation schemes for monotone systems of fully nonlinear second order partial differential equations. We first 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 finite difference schemes and Semi-Lagrangian schemes are discussed.

Approximation schemes for monotone systems of nonlinear second order partial differential equations: convergence result and error estimate / Ariela, Briani; Camilli, Fabio; Hasnaa, Zidani. - In: DIFFERENTIAL EQUATIONS & APPLICATIONS. - ISSN 1847-120X. - STAMPA. - 4:2(2012), pp. 297-317. [10.7153/dea-04-18]

Approximation schemes for monotone systems of nonlinear second order partial differential equations: convergence result and error estimate

CAMILLI, FABIO;
2012

Abstract

We consider approximation schemes for monotone systems of fully nonlinear second order partial differential equations. We first 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 finite difference schemes and Semi-Lagrangian schemes are discussed.
2012
approximation scheme; error estimate.; monotone systems; viscosity solution
01 Pubblicazione su rivista::01a Articolo in rivista
Approximation schemes for monotone systems of nonlinear second order partial differential equations: convergence result and error estimate / Ariela, Briani; Camilli, Fabio; Hasnaa, Zidani. - In: DIFFERENTIAL EQUATIONS & APPLICATIONS. - ISSN 1847-120X. - STAMPA. - 4:2(2012), pp. 297-317. [10.7153/dea-04-18]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/454956
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