On the application of the Arlequin method to the coupling of particle and continuum models

In this work, we propose to extend the Arlequin framework to couple particle and continuum models. Three different coupling strategies are investigated based on the L-2 norm, H-1 seminorm, and H-1 norm. The mathematical properties of the method are studied for a one-dimensional model of harmonic springs, with varying coefficients, coupled with a linear elastic bar, whose modulus is determined by simple homogenization. It is shown that the method is well-posed for the H-1 seminorm and H-1 norm coupling terms, for both the continuous and discrete formulations. In the case of L-2 coupling, it cannot be shown that the Babuska-Brezzi condition holds for the continuous formulation. Numerical examples are presented for the model problem that illustrate the approximation properties of the different coupling terms and the effect of mesh size.