Overlapping Nonmatching Grid Method for the Ergodic Control Quasi Variational Inequalities

H. Mécheri, S. Saadi

Department of Mathematics, Badji Mokhtar University, Annaba, Algeria.

DOI: 10.4236/ajcm.2013.31A005                

Abstract

In this paper, we provide a maximum norm analysis of an overlapping Schwarz method on nonmatching grids for a quasi-variational inequalities related to ergodic control problems studied by M. Boulbrachene [1], where the “discount factor” (i.e., the zero order term) is set to 0, we use an overlapping Schwarz method on nonmatching grid which consists in decomposing the domain in two sub domains, where the discrete alternating Schwarz sequences in sub domains converge to the solution of the ergodic control IQV for the zero order term. For and under a discrete maximum principle we show that the discretization on each sub domain converges quasi-optimally in the norm to 0.

Keywords

Quasi Variational Inequalities; Ergodic Control; Schwarz Method; Finite Element Method

Conflicts of Interest

The authors declare no conflicts of interest.

References

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