Introducing a coupling framework reminiscent of FETI methods, but here on abstract form, we establish conditions for stability and minimal requirements for well-posedness on the continuous level, as well as conditions on local solvers for the approximation of subproblems. We then discuss stability of the resulting Lagrange multiplier methods and show stability under a mesh conditions between the local discretizations and the mortar space. If this condition is not satisfied we show how a stabilization, acting only on the multiplier can be used to achieve stability. The design of preconditioners of the Schur complement system is discussed in the unstabilized case. Finally we discuss some applications that enter the framework.

翻译：引入一种类似于FETI方法的耦合框架，但此处采用抽象形式。我们在连续层面上建立了稳定性条件及适定性所需的最少要求，同时给出了子问题近似的局部求解器条件。随后讨论了所得拉格朗日乘子法的稳定性，并展示了在局部离散化与接触空间满足网格条件时的稳定性。若不满足该条件，我们展示了如何通过仅作用于乘子的稳定化来实现稳定性。在非稳定情况下，讨论了舒尔补系统预处理子的设计。最后，探讨了该框架下的若干应用实例。