A continuous framework for FETI-DP with a mesh independent condition number for the dual problem

We present an abstract setting for a variation of the FETI-DP method applied to second order elliptic problems. In this setting, the matrix iteration for the dual problem has a mesh independent condition number. This work improves the ideas recently introduced by Bernardi et al. [C. Bernardi, T. Chacón Rebollo, E. Chacón Vera, A FETI method with a mesh independent condition number for the iteration matrix, Comput. Methods Appl. Mech. Engrg. 197 (13–16) (2008) 1410–1429]. The continuity restrictions for the displacement field across interfaces are weakly imposed using the natural trace norm instead of pointwise continuity. gh a slight coupling between subdomains is introduced, still a parallel computation is possible. Some numerical tests are also performed to illustrate the method.