Abstract
The solution of the biharmonic equation with an homogeneous boundary conditions is decomposed into a regular part and a singular one. The later is written as a coefficient multiplied by the first singular function associated to the bilaplacian operator. In this paper, we consider the dual singular method for finding the value of the leading singular coefficient, and we use the mortar domain decomposition technique with the spectral discretization for its approximation. The numerical analysis leads to optimal error estimates. We present some numerical results which are in perfect coherence with the analysis developed in this paper.