Calculus of Variations and Geometric Measure Theory

A. Briani - F. Camilli - H. Zidani

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

created by briani on 25 Jul 2011
modified on 22 Mar 2012

[BibTeX]

Published Paper

Inserted: 25 jul 2011
Last Updated: 22 mar 2012

Journal: Differ. Equ. Appl.
Volume: 4
Pages: 297-317
Year: 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.


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