Correction: Neumann-Neumann type domain decomposition of elliptic problems on metric graphs

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

Authors

Institutions

Publication Details

Journal
BIT Numerical Mathematics
Published
2025-07-14
DOI
https://doi.org/10.1007/s10543-025-01076-7
Primary Topic
Advanced Mathematical Modeling in Engineering
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Correction: Neumann-Neumann type domain decomposition of elliptic problems on metric graphs

Mihály Kovács, Mihály A. Vághy
BIT Numerical Mathematics
Advanced Mathematical Modeling in Engineering
article

Correction: Neumann-Neumann type domain decomposition of elliptic problems on metric graphs

Mihály Kovács, Mihály A. Vághy
article en

Abstract

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

BIT Numerical MathematicsVol. 65(3)
Budapest University of Technology and Economics (HU), Pázmány Péter Catholic University (HU), Chalmers University of Technology (SE)
Openalex Percentile: Top 82%
Advanced Mathematical Modeling in Engineering
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.