A Tensor-Product Finite Element Cochain Complex with Arbitrary Continuity
arXiv:2207.00309 · doi:10.23967/eccomas.2022.134
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 -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.