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In this paper,we propose two BDDC preconditioners for the mortar-type rotated Q1 finite element method for second order elliptic partial differential equations with piecewise but discontinuous coefficients.We construct an auxiliary discrete space and build our method based on an equivalent auxiliary problem,we present the BDDC preconditioners based on this constructed discrete space.Meanwhile,in the framework of the standard additive Schwarz methods,we describe this method by a complete variational form.