CONFORMING FINITE ELEMENT DIVDIV COMPLEXES AND THE APPLICATION FOR THE LINEARIZED EINSTEIN-BIANCHI SYSTEM

Jun Hu; Yizhou Liang; Rui Ma

doi:10.1137/21M1404235

CONFORMING FINITE ELEMENT DIVDIV COMPLEXES AND THE APPLICATION FOR THE LINEARIZED EINSTEIN-BIANCHI SYSTEM

Jun Hu, Yizhou Liang, Rui Ma

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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 H(div div, Ω; S) are from a recent article [L. Chen and X. Huang, Math. Comp., 91 (2022), pp. 1107-1142] while finite element spaces of both H(sym curl, Ω; T) and H¹(Ω; ℝ³) 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 Einstein-Bianchi system within the dual formulation.

Original language	English
Pages (from-to)	1307-1330
Number of pages	24
Journal	SIAM Journal on Numerical Analysis
Volume	60
Issue number	3
DOIs	https://doi.org/10.1137/21M1404235
Publication status	Published - 2022
Externally published	Yes

Keywords

H(symcurl) conforming finite element
divdiv complex
linearized Einstein-Bianchi system

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10.1137/21M1404235

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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 H(div div, Ω; S) are from a recent article [L. Chen and X. Huang, Math. Comp., 91 (2022), pp. 1107-1142] while finite element spaces of both H(sym curl, Ω; T) and H1(Ω; ℝ3) 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 Einstein-Bianchi system within the dual formulation.",

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PY - 2022

Y1 - 2022

N2 - 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 H(div div, Ω; S) are from a recent article [L. Chen and X. Huang, Math. Comp., 91 (2022), pp. 1107-1142] while finite element spaces of both H(sym curl, Ω; T) and H1(Ω; ℝ3) 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 Einstein-Bianchi system within the dual formulation.

AB - 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 H(div div, Ω; S) are from a recent article [L. Chen and X. Huang, Math. Comp., 91 (2022), pp. 1107-1142] while finite element spaces of both H(sym curl, Ω; T) and H1(Ω; ℝ3) 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 Einstein-Bianchi system within the dual formulation.

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KW - linearized Einstein-Bianchi system

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CONFORMING FINITE ELEMENT DIVDIV COMPLEXES AND THE APPLICATION FOR THE LINEARIZED EINSTEIN-BIANCHI SYSTEM

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Keywords

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