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

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 semiimplicit time scheme combined with a FInite element spatial approximation. Also the techniques of the residual a posteriori error analysis are used. Moreover, using BenssoussanLions algorithm, an asymptotic behavior in H^1_0 norm is deduced. Furthermore, the results of some numerical experiments are presented to support the theory.