Construction of finite element differential complexes by tensor products

Guido Kanschat (U Heidelberg)

May 20. 2026, 10:45 — 11:30

We begin with a general lemma establishing that a finite element subcomplex of a differential complex can be constructed by choosing commutating degrees of freedom and matching basis functions. Applying this lemma, we construct one-dimensional finite element complexes of arbitrary order and continuity, using a modified Hermite interpolation. We then discuss the tensor product construction of differential forms. The general lemma will allow us to combine this construction with a generic definition of tensor product node functionals to obtain commuting interpolation operators in arbitrary dimensions. Using an argument about linear functionals on tensor products of Hilbert spaces, we obtain bounded quasi-interpolation operators on L2

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Differential Complexes: Theory, Discretization, and Applications (Thematic Programme)
Organizer(s):
Andreas Cap (U of Vienna)
Ralf Hiptmair (ETH Zurich)
Kaibo Hu (U of Oxford)
Joachim Schöberl (TU Wien)