Corpus ID: 232076213

# 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}
}
• Published 26 February 2021
• Computer Science, Mathematics
• ArXiv
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… Expand
1 Citations
Conforming Finite Elements for $H(\text{sym}\,\text{Curl})$ and $H(\text{dev}\,\text{sym}\,\text{Curl})$
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#### References

SHOWING 1-10 OF 16 REFERENCES
Finite elements for divdiv-conforming symmetric tensors
• Mathematics, Computer Science
• ArXiv
• 2020
Two types of finite element spaces on triangles are constructed for div-div conforming symmetric tensors and they are exploited to discretize the mixed formulation of the biharmonic equation. Expand
Finite elements for divdiv-conforming symmetric tensors in three dimensions
• Mathematics, Computer Science
• ArXiv
• 2020
Two types of finite element spaces on a tetrahedron are constructed for divdiv conforming symmetric tensors in three dimensions and several decomposition of polynomial vector and tensors spaces are revealed from the complexes. Expand
Nodal finite element de Rham complexes
• Mathematics, Computer Science
• Numerische Mathematik
• 2018
It is shown how regularity decreases in the finite element complexes, so that they branch into known complexes, and the standard de Rham complexes of Whitney forms can be regarded as the family with the lowest regularity. Expand
A new approach to finite element simulations of general relativity
This dissertation presents a meta-modelling system that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of manually cataloging and calculating the discrete-time steps of theorems. Expand
• Computer Science, Mathematics
• Math. Comput.
• 2021
The first family of conforming discrete three dimensional Gradgrad-complexes consisting of finite element spaces is constructed, which can be used in the mixed form of the linearized Einstein-Bianchi system. Expand
A family of mixed finite elements for the biharmonic equations on triangular and tetrahedral grids
• Computer Science, Mathematics
• Science China Mathematics
• 2021
A new family of mixed finite elements for solving a mixed formulation of the biharmonic equations in two and three dimensions and the optimal order of convergence is achieved. Expand
Discrete Hessian complexes in three dimensions
• Computer Science, Physics
• ArXiv
• 2020
One conforming and one non-conforming virtual element Hessian complexes on tetrahedral grids are constructed based on decompositions of polynomial tensor space. They are applied to discretize theExpand
An ultraweak formulation of the Kirchhoff-Love plate bending model and DPG approximation
• Mathematics, Computer Science
• Math. Comput.
• 2019
An ultraweak variational formulation for a variant of the Kirchhoff-Love plate bending model is developed and a discretization of the discontinuous Petrov-Galerkin type with optimal test functions (DPG) is introduced, proving well-posedness of the ultraweak formulation and quasi-optimal convergence of the DPG scheme. Expand
Fully discrete DPG methods for the Kirchhoff–Love plate bending model
• Mathematics
• Computer Methods in Applied Mechanics and Engineering
• 2019
We extend the analysis and discretization of the Kirchhoff-Love plate bending problem from [T. F\"uhrer, N. Heuer, A.H. Niemi, An ultraweak formulation of the Kirchhoff-Love plate bending model andExpand