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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. | 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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| + | == Abstract == | ||
| + | <pdf>Media:Draft_Test_395607766824_abstract.pdf</pdf> | ||
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| + | == Full Paper == | ||
| + | <pdf>Media:Draft_Test_395607766824_paper.pdf</pdf> | ||
Latest revision as of 08:59, 25 November 2022
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 25/11/22
Submitted on 25/11/22
Licence: CC BY-NC-SA license
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