An abstract framework for heterogeneous coupling: stability, approximation and preconditioning
Abstract
We consider heterogeneous coupling problems on an abstract level, establishing fundamental principles of domain decomposition agnostic to the solvers of the local subproblems. 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 condition 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.
Cite
@article{arxiv.2312.11733,
title = {An abstract framework for heterogeneous coupling: stability, approximation and preconditioning},
author = {Silvia Bertoluzza and Erik Burman},
journal= {arXiv preprint arXiv:2312.11733},
year = {2026}
}