Algorithmic realization of the solution to the sign conflict problem for hanging nodes on hp-hexahedral N\'ed\'elec elements
Numerical Analysis
2024-07-12 v2 Numerical Analysis
Abstract
In this work, N\'ed\'elec 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 N\'ed\'elec 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
Cite
@article{arxiv.2306.01416,
title = {Algorithmic realization of the solution to the sign conflict problem for hanging nodes on hp-hexahedral N\'ed\'elec elements},
author = {Sebastian Kinnewig and Thomas Wick and Sven Beuchler},
journal= {arXiv preprint arXiv:2306.01416},
year = {2024}
}