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 onedimensional Cm-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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Published on 22/11/22

Volume Computational Applied Mathematics, 2022
DOI: 10.23967/eccomas.2022.134
Licence: CC BY-NC-SA license

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