Summary: A MULTISCALE MORTAR MIXED SPACE
BASED ON HOMOGENIZATION
FOR HETEROGENEOUS ELLIPTIC PROBLEMS
TODD ARBOGAST AND HAILONG XIAO
Abstract. We consider a second order elliptic problem with a heterogeneous coefficient written
in mixed form. The nonoverlapping mortar domain decomposition method is efficient in parallel if the
mortar interface coupling space has a restricted number of degrees of freedom. In the heterogeneous
case, we define a new multiscale mortar space that incorporates information from homogenization
theory to better approximate the solution along the interfaces with just a few degrees of freedom.
In the case of a locally periodic heterogeneous coefficient of period , we prove that the new method
achieves both optimal order error estimates in the discretization parameters and convergence when
is small, with no numerical resonance, despite the fact that our method is purely locally defined.
Moreover, we present three numerical examples to assess its performance when the coefficient is
not obviously locally periodic. We show that the new mortar method works well, and better than
polynomial mortar spaces.
Key words. nonoverlapping domain decomposition, mixed method, multiscale finite element,
multiscale mortar, convergence, numerical resonance
AMS subject classifications. 65N15, 65N30, 65N55, 76M50, 76S05
1. Introduction. Domain decomposition methods for partial differential equa-
tions have been developed as a linear solver strategy that increases parallelism. We