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Résolution numérique d'inégalités variationnelles: Localisation avec conditions de Dirichlet

Volume 14, Number 1 (2012), 1 - 23

Résolution numérique d'inégalités variationnelles: Localisation avec conditions de Dirichlet

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Abstract

In this paper we present an approximation of viscosity solution of non linear partial differential equation with dirichlet bounded conditions. Our approach used a fully nonlinear PDE in an unbounded domain. To approximate its unique viscosity solution one needs to localize the PDE under consideration and to define artificial boundary conditions. It is known that backward stochastic differential equations (BSDEs) are a useful tool to estimate the error due to misspecified Dirichlet boundary conditions on the artificial boundary [12], but we perfect in this paper their approximation of localization error.