# Asymptotic behavior and a posteriori error estimates in Sobolev space for the generalized overlapping domain decomposition method for evolutionary HJB equation with nonlinear source terms. Part 1

Volume 9, Issue 3, pp 736--756 Publication Date: March 24, 2016
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### Authors

Salah Boulaaras - Department Of Mathematics, College Of Sciences and Arts, Al-Qassim University, Al-Rass, Kingdom Of Saudi Arabia.

### Abstract

A posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet boundary conditions on the boundaries for the discrete solutions on subdomains of evolutionary HJB equation with nonlinear source terms are established using the semi-implicit time scheme combined with a FInite element spatial approximation. Also the techniques of the residual a posteriori error analysis are used. Moreover, using Benssoussan-Lions' algorithm, an asymptotic behavior in $H^1_0$-norm is deduced. Furthermore, the results of some numerical experiments are presented to support the theory.

### Keywords

• A posteriori error estimates
• GODDM
• Dirichlet boundary conditions
• algorithm
• asymptotic behavior.

•  65N06
•  65N12
•  65F05

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