# Conforming finite element DIVDIV complexes and the application for the linearized Einstein-Bianchi system

@article{Hu2021ConformingFE, title={Conforming finite element DIVDIV complexes and the application for the linearized Einstein-Bianchi system}, author={Jun Hu and Yizhou Liang and Rui Ma}, journal={ArXiv}, year={2021}, volume={abs/2103.00088} }

Abstract. This paper presents the first family of conforming finite element div div complexes on tetrahedral grids in three dimensions. In these complexes, finite element spaces of Hpdiv div,Ω; Sq are from a current preprint [Chen and Huang, arXiv: 2007.12399, 2020] while finite element spaces of both Hpsym curl,Ω;Tq and HpΩ;Rq are newly constructed here. It is proved that these finite element complexes are exact. As a result, they can be used to discretize the linearized EinsteinBianchi system…

## 2 Citations

Conforming Finite Elements for $H(\text{sym}\,\text{Curl})$ and $H(\text{dev}\,\text{sym}\,\text{Curl})$

- Mathematics, Computer Science
- 2021

This work constructs conforming finite elements for the spaces H(sym Curl) and H(dev sym Curl), and shows the construction, proves conformity and unisolvence, and point out optimal approximation error bounds.

Geometric Decompositions of Div-Conforming Finite Element Tensors

- Computer Science, MathematicsArXiv
- 2021

A unified construction of div-conforming finite element tensors, including vector div element, symmetric div matrix element, traceless div matrix element, and in general tensors with constraints, is…

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