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.
Highlights
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping sub domains.The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the sub domain.In this paper, we are interested in the error analysis in the maximum norm for the obstacle problem in the context of overlapping nonmatching grids: we consider a domain Ω which is the union of two overlapping subdoains where each sub domain has its own triangulation
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
Boulbrachène [1], where the “discount factor” 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
Summary
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping sub domains. We are interested in the error analysis in the maximum norm for the obstacle problem in the context of overlapping nonmatching grids: we consider a domain Ω which is the union of two overlapping subdoains where each sub domain has its own triangulation. This kind of discretizations is very interesting as they can be applied to solving many practical problems which cannot be handled by global discretizations. Perthame [3] quasi-variational inequalities and ergodic impulse control
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