Finite element form-valued forms: A unified construction
Vortrag von Ting Lin
Datum: 07.05.25 Zeit: 16.30 - 18.00 Raum: ETH HG G 19.2
We provide a finite element discretization of $\ell$-form-valued $k$ form in $n$ dimensions for general $k$, $\ell$ and $n$ and polynomial degree. The construction generalizes finite element Whitney forms for the de~Rham complex and their higher-order and distributional versions, the Regge finite elements and the Christiansen--Regge elasticity complex, the TDNNS element for symmetric stress tensors, the MCS element for traceless matrix fields, the Hellan--Herrmann--Johnson (HHJ) elements for biharmonic equations, and discrete divdiv and Hessian complexes in [Hu, Lin, and Zhang, 2025]. The construction discretizes the Bernstein--Gelfand--Gelfand (BGG) diagrams. Applications of the construction include discretization of strain and stress tensors in continuum mechanics and metric and curvature tensors in differential geometry in any dimension. This talk is based on a joint work with Kaibo Hu (Edinburgh).