Correction: Neumann-Neumann type domain decomposition of elliptic problems on metric graphs
Mihály Kovács, Mihály A. Vághy · BIT Numerical Mathematics · 2025
In the original version of this article, a text from Sect.4.2 has been typeset as the content of the Conclusion section by mistake.The correct Conclusion section reads as follows:A Neumann-Neumann type domain decomposition method was developed for elliptic problems on metric graphs.We have defined the iteration in the continuous and discrete setting and rewritten the latter as a preconditioner for the Schur complement system.The discrete iteration was then formulated as an abstract additive Schwarz iteration and we proved that it converges to the finite element solution with a rate that is independent of the finite element mesh size.Moreover, we have shown that the condition number of the Schur complement is uniformly bounded with respect to the finite element mesh size with a bound that depends on the maximum degree.We implemented the algorithm along with a diagonal and polynomial preconditioners and tested them on various examples.The numerical results confirm our theoretical results regarding the condition number of the Schur complement and that of the