Two non-overlapping domain decomposition methods are presented for the mixedfinite element formulation of linear elasticity with weakly enforced stresssymmetry. The methods utilize either displacement or normal stress Lagrangemultiplier to impose interface continuity of normal stress or displacement,respectively. By eliminating the interior subdomain variables, the globalproblem is reduced to an interface problem, which is then solved by aniterative procedure. The condition number of the resulting algebraic interfaceproblem is analyzed for both methods. A multiscale mortar mixed finite elementmethod for the problem of interest on non-matching multiblock grids is alsostudied. It uses a coarse scale mortar finite element space on the non-matchinginterfaces to approximate the trace of the displacement and impose weakly thecontinuity of normal stress. A priori error analysis is performed. It is shownthat, with appropriate choice of the mortar space, optimal convergence on thefine scale is obtained for the stress, displacement, and rotation, as well assome superconvergence for the displacement. Computational results are presentedin confirmation of the theory of all proposed methods.
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