A stabilized discontinuous mortar formulation for elastostatics and elastodynamics problems Part I: abstract framework

In this paper, we first recall the general assumptions and results arising in mortar methods applied to elastostatics [Woh01]. By extension to the curved interfaces case of the ideas from Gopalakrishnan and Brenner [Gop99, Bre03, Bre04], and from the introduction a generalized Scott and Zhang interpolation operator [SZ90], we prove the independence of the coercivity constant of the broken elasticity bilinear form with respect to the number and the size of the subdomains. Moreover, we extend the proof of optimal convergence to the elastodynamic framework. The present results are applied in Part II (discontinuous Lagrange multipliers), in which a stabilized discontinuous formulation is proposed, analyzed and tested.