A Tensor-Product Finite Element Cochain Complex with Arbitrary Continuity

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Bonizzoni, Francesca, Kanschat, Guido
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 01.07.2022
Subjects
Cartesian coordinates
Commutation
Computer Science - Numerical Analysis
Interpolation
Mathematical analysis
Mathematics - Numerical Analysis
Operators (mathematics)
Smoothness
Tensors
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2207.00309