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Mathematics > Numerical Analysis

arXiv:2207.00309 (math)
[Submitted on 1 Jul 2022]

Title:A Tensor-Product Finite Element Cochain Complex with Arbitrary Continuity

Authors:Francesca Bonizzoni, Guido Kanschat
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Abstract:We develop tensor product finite element cochain complexes of arbitrary smoothness on Cartesian meshes of arbitrary dimension. The first step is the construction of a one-dimensional $C^m$-conforming finite element cochain complex based on a modified Hermite interpolation operator, which is proved to commute with the exterior derivative by means of a general commutation lemma. Adhering to a strict tensor product construction we then derive finite element complexes in higher dimensions.
Subjects: Numerical Analysis (math.NA)
MSC classes: 65N30
Cite as: arXiv:2207.00309 [math.NA]
  (or arXiv:2207.00309v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2207.00309
Related DOI: https://doi.org/10.23967/eccomas.2022.134

Submission history

From: Guido Kanschat [view email]
[v1] Fri, 1 Jul 2022 09:56:48 UTC (11 KB)
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