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Add support for hanging nodes to the NedelecSZ class. #16304

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merged 4 commits into from
Jan 21, 2024
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Add support for hanging nodes to the NedelecSZ class. #16304

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70407c1
Add support for hanging nodes to the NedelecSZ class.
May 19, 2023
dfd5f53
Add a convergence test that verifies that hanging nodes on FE_Nedelec…
Dec 8, 2023
9d7a3e0
Added new test case based on fe_nedelec_sz_gradient_divergence_theorem.
Jan 15, 2024
f16f94d
Add another test to verify that inhomogeneous boundary conditions wit…
Jan 15, 2024
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3 changes: 3 additions & 0 deletions doc/news/changes/major/20231128SebastianKinnewig
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New: Support for hanging nodes in FE_NedelecSZ.
<br>
(Sebastian Kinnewig, 2023/11/28)
11 changes: 10 additions & 1 deletion include/deal.II/fe/fe_nedelec_sz.h
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Expand Up @@ -63,13 +63,22 @@ DEAL_II_NAMESPACE_OPEN
* vertices are decided such that the second has a higher global vertex
* numbering than the fourth.
*
* Note that this element does not support non-conforming meshes at this time.
* To overcome the sign conflict in the case of non-conforming meshes, hanging
* edges (and faces in 3D) must be addressed. This element chooses the
* orientation of hanging edges (and faces) based on the parent cell. Moreover,
* the associated constraint matrix that restricts the additional DoFs
* originating from the hanging edges and faces must be adapted to account for
* the orientation of the edges and faces.
*
* Further details on this element, including some benchmarking, can be
* in the paper R. Kynch, P. Ledger: <b>Resolving the sign conflict
* problem for hp-hexahedral N&eacute;d&eacute;lec elements with application to
* eddy current problems</b>, Computers & Structures 181, 41-54, 2017 (see
* https://doi.org/10.1016/j.compstruc.2016.05.021).
* For details on the implementation of the hanging node constraints, see the
* paper S. Kinnewig, T. Wick, S. Beuchler: <b>Algorithmic realization of the
* solution to the sign conflict problem for hanging nodes on hp-hexahedral
* Nédélec elements</b>, preprint, 2023 (https://arxiv.org/abs/2306.01416).
*/
template <int dim, int spacedim = dim>
class FE_NedelecSZ : public FiniteElement<dim, dim>
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