Iterative substructuring preconditioners for mortar element methods in twodimensions

The mortar methods are based on domain decomposition and they allow for the coupling of different variational approximations in different subdomains. The resulting methods are nonconforming but still yield optimal approximati ons. In this paper, we will discuss iterative substructuring algorithms for the algebraic systems arising from the discretization of symmetric, second -order, elliptic equations in two dimensions. Both spectral and finite elem ent methods, for geometrically conforming as well as nonconforming domain d ecompositions, are studied. In each case, we obtain a polylogarithmic bound on the condition number of the preconditioned matrix.