2025-07-03 Thursday Sign in CN

Activities
Finite element form-valued forms
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Reporter:
Kaibo Hu, Royal Society University Research Fellow, The University of Edinburgh
Inviter:
Shipeng Mao, Professor
Subject:
Finite element form-valued forms
Time and place:
14:00-15:00 July 15(Tuesday), S615
Abstract:

We provide a finite element discretization of $\ell$-form-valued $k$-forms on triangulation in $\mathbb{R}^{n}$ for general $k$, $\ell$ and $n$ and any polynomial degree. The construction generalizes finite element Whitney forms for the de~Rham complex and their high-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.