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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Published in | arXiv.org |
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Main Authors | , |
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Language | English |
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01.07.2022
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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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AbstractList | 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. 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. |
Author | Bonizzoni, Francesca Kanschat, Guido |
Author_xml | – sequence: 1 givenname: Francesca surname: Bonizzoni fullname: Bonizzoni, Francesca – sequence: 2 givenname: Guido surname: Kanschat fullname: Kanschat, Guido |
BackLink | https://doi.org/10.23967/eccomas.2022.134$$DView published paper (Access to full text may be restricted) https://doi.org/10.48550/arXiv.2207.00309$$DView paper in arXiv |
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DOI | 10.48550/arxiv.2207.00309 |
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Snippet | We develop tensor product finite element cochain complexes of arbitrary smoothness on Cartesian meshes of arbitrary dimension. The first step is the... We develop tensor product finite element cochain complexes of arbitrary smoothness on Cartesian meshes of arbitrary dimension. The first step is the... |
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SubjectTerms | Cartesian coordinates Commutation Computer Science - Numerical Analysis Interpolation Mathematical analysis Mathematics - Numerical Analysis Operators (mathematics) Smoothness Tensors |
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Title | A Tensor-Product Finite Element Cochain Complex with Arbitrary Continuity |
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