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P. G. Ciarlet and P. A. Raviart, “Maximum Principle and Uniform Convergence for the Finite Element Method,” Computer Methods in Applied Mechanics and Engineering, Vol. 2, No. 1, 1973, pp. 17-31.

has been cited by the following article:

• TITLE: Overlapping Nonmatching Grid Method for the Ergodic Control Quasi Variational Inequalities

  AUTHORS: H. Mécheri, S. Saadi

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

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.1A, April 30, 2013

  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.