Details
| Original language | English |
|---|---|
| Article number | 23 |
| Number of pages | 20 |
| Journal | ACM Transactions on Mathematical Software |
| Volume | 51 |
| Issue number | 4 |
| Early online date | 10 Sept 2025 |
| Publication status | Published - 12 Dec 2025 |
Abstract
In this work, Nédélec elements on locally refined meshes with hanging nodes are considered. A crucial aspect is the orientation of the hanging edges and faces. For non-orientable meshes, no solution or implementation has been available to date. The problem statement and corresponding algorithms are described in great detail. As a model problem, the time-harmonic Maxwell’s equations are adopted because Nédélec elements constitute their natural discretization. The algorithms and implementation are demonstrated through two numerical examples on different uniformly and adaptively refined meshes. The implementation is performed within the finite element library deal.II.
Keywords
- Finite element method, hanging nodes, locally refined meshes, Nédélec elements, sign-conflict, time-harmonic Maxwell’s equations
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Mathematics(all)
- Applied Mathematics
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In: ACM Transactions on Mathematical Software, Vol. 51, No. 4, 23, 12.12.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Algorithmic Realization of the Solution to the Sign Conflict Problem for Hanging Nodes on Hp-Hexahedral Nédélec Elements
AU - Kinnewig, Sebastian
AU - Wick, Thomas
AU - Beuchler, Sven
N1 - Publisher Copyright: © 2025 Copyright held by the owner/author(s).
PY - 2025/12/12
Y1 - 2025/12/12
N2 - In this work, Nédélec elements on locally refined meshes with hanging nodes are considered. A crucial aspect is the orientation of the hanging edges and faces. For non-orientable meshes, no solution or implementation has been available to date. The problem statement and corresponding algorithms are described in great detail. As a model problem, the time-harmonic Maxwell’s equations are adopted because Nédélec elements constitute their natural discretization. The algorithms and implementation are demonstrated through two numerical examples on different uniformly and adaptively refined meshes. The implementation is performed within the finite element library deal.II.
AB - In this work, Nédélec elements on locally refined meshes with hanging nodes are considered. A crucial aspect is the orientation of the hanging edges and faces. For non-orientable meshes, no solution or implementation has been available to date. The problem statement and corresponding algorithms are described in great detail. As a model problem, the time-harmonic Maxwell’s equations are adopted because Nédélec elements constitute their natural discretization. The algorithms and implementation are demonstrated through two numerical examples on different uniformly and adaptively refined meshes. The implementation is performed within the finite element library deal.II.
KW - Finite element method
KW - hanging nodes
KW - locally refined meshes
KW - Nédélec elements
KW - sign-conflict
KW - time-harmonic Maxwell’s equations
UR - http://www.scopus.com/inward/record.url?scp=105025977624&partnerID=8YFLogxK
U2 - 10.1145/3766903
DO - 10.1145/3766903
M3 - Article
AN - SCOPUS:105025977624
VL - 51
JO - ACM Transactions on Mathematical Software
JF - ACM Transactions on Mathematical Software
SN - 0098-3500
IS - 4
M1 - 23
ER -