Open AccessAsymptotic 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
Author(s) -
Salah Boulaaras
Publication year - 2016
Publication title -
the journal of nonlinear sciences and applications
Language(s) - English
Resource type - Journals
eISSN - 2008-1901
pISSN - 2008-1898
DOI - 10.22436/jnsa.009.03.03
Subject(s) - mathematics , sobolev space , hamilton–jacobi–bellman equation , a priori and a posteriori , nonlinear system , domain decomposition methods , domain (mathematical analysis) , space (punctuation) , decomposition , mathematical analysis , mathematical optimization , finite element method , computer science , philosophy , ecology , physics , epistemology , quantum mechanics , biology , thermodynamics , optimal control , operating system
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 H1 0 -norm is deduced. Furthermore, the results of some numerical experiments are presented to support the theory. c ©2016 All rights reserved.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom