Additive Schwarz methods for elliptic mortar finite element problems

Two variants of the additive Schwarz method for solving linear systems arising from the mortar finite element discretization on nonmatching meshes of second order elliptic problems with discontinuous coefficients are designed and analyzed. The methods are defined on subdomains without overlap, and they use special coarse spaces, resulting in algorithms that are well suited for parallel computation. The condition number estimate for the preconditioned system in each method is proportional to the ratio H/h, where H and h are the mesh sizes, and it is independent of discontinuous jumps of the coefficients. For one of the methods presented the choice of the mortar (nonmortar) side is independent of the coefficients.