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arXiv · 2207.00309

A Tensor-Product Finite Element Cochain Complex with Arbitrary Continuity

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.

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Francesca Bonizzoni, Guido Kanschat. 2022-07-01. A Tensor-Product Finite Element Cochain Complex with Arbitrary Continuity. https://doi.org/10.23967/eccomas.2022.134

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