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 | |
| Publication status | Published - 2022 |
| Externally published | Yes |
Keywords
- H(symcurl) conforming finite element
- divdiv complex
- linearized Einstein-Bianchi system
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Hu, J., Liang, Y., & Ma, R. (2022). CONFORMING FINITE ELEMENT DIVDIV COMPLEXES AND THE APPLICATION FOR THE LINEARIZED EINSTEIN-BIANCHI SYSTEM. SIAM Journal on Numerical Analysis, 60(3), 1307-1330. https://doi.org/10.1137/21M1404235