  In this paper, we extend the additive average Schwarz method to solve second
order elliptic boundary value problems with heterogeneous coefficients inside
the subdomains and across their interfaces by the mortar technique, where the
mortar finite element discretization is on nonmatching meshes. In this
two-level method, we enrich the coarse space in two different ways, i.e., by
adding eigenfunctions of two variants of the generalized eigenvalue problems.
We prove that the condition numbers of the systems of algebraic equations
resulting from the extended additive average Schwarz method, corresponding to
both coarse spaces, are of the order O(H/h) and independent of jumps in the
coefficients, where H and h are the mesh parameters.
