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The mortar element method with overlapping Yves Achdou

Summary: The mortar element method with overlapping
Yves Achdou 
Yvon Maday y
July 12, 2001
In this paper, we discuss an extension of the mortar element method to overlapping
subdomains and nonmatching grids in the overlapped zones. We discuss in particular the
case where more than two subdomains overlap. The method is described and analyzed.
Also, some preconditioned iterative methods for solving the linear systems arising from this
discretization are described and analyzed.
1 Introduction
The mortar element methods were introduced in [4] for non overlapping domain decompositions
in order to couple di erent variational approximations in di erent subdomains. In the nite
element context, one important advantage of the mortar element methods is that they allow for
using structured grids in subdomains thus fast solvers [1]. The resulting methods are noncon-
forming but still yield optimal approximations. The literature on the mortar element methods
is growing numerous see [2] and reference therein.
In this paper, we shall discuss the case of overlapping subdomains, with meshes constructed
in an independent manner in each subdomain. As pointed by F. Hecht, J.L. Lions, and O.


Source: Achdou, Yves - Laboratoire Jacques-Louis Lions, Université Pierre-et-Marie-Curie, Paris 6


Collections: Mathematics