In this work, we solve a long-standing open problem: Is it true that the convergence rate of the Lions' Robin-Robin nonoverlapping domain decomposition(DD) method can be constant, independent of the mesh size h? We closed this twenty-year old problem with a positive answer. Our theory is also verified by numerical tests.
@article{arxiv.1112.4327,
title = {On the optimal convergence rate of a Robin-Robin domain decomposition method},
author = {Wenbin Chen and Xuejun Xu and Shangyou Zhang},
journal= {arXiv preprint arXiv:1112.4327},
year = {2012}
}