A family of conforming finite element divdiv complexes on cuboid meshes

Jun Hu; Yizhou Liang; Rui Ma; Min Zhang

doi:10.1007/s00211-024-01418-7

A family of conforming finite element divdiv complexes on cuboid meshes

Jun Hu
, Yizhou Liang
, Rui Ma
, Min Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Peking University
Chongqing Research Institute of Big Data
China Academy of Engineering Physics

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

1 Citation (Scopus)

Abstract

In this paper, the first family of conforming finite element divdiv complexes on cuboid meshes is constructed. The complex exhibits exactness on a contractible domain in the sense that the kernel space of each successive discrete map is the range of the previous one. This allows for algebraic structure-preserving finite element discretization of both the biharmonic equation and the linearized Einstein–Bianchi system. The convergence of optimal order is established and validated through numerical examples.

Original language	English
Pages (from-to)	1603-1638
Number of pages	36
Journal	Numerische Mathematik
Volume	156
Issue number	4
DOIs	https://doi.org/10.1007/s00211-024-01418-7
Publication status	Published - Aug 2024

Keywords

35B45
65N12
65N15
65N30
Primary 65M60

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10.1007/s00211-024-01418-7

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abstract = "In this paper, the first family of conforming finite element divdiv complexes on cuboid meshes is constructed. The complex exhibits exactness on a contractible domain in the sense that the kernel space of each successive discrete map is the range of the previous one. This allows for algebraic structure-preserving finite element discretization of both the biharmonic equation and the linearized Einstein{\textendash}Bianchi system. The convergence of optimal order is established and validated through numerical examples.",

keywords = "35B45, 65N12, 65N15, 65N30, Primary 65M60",

author = "Jun Hu and Yizhou Liang and Rui Ma and Min Zhang",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.",

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AU - Liang, Yizhou

AU - Ma, Rui

AU - Zhang, Min

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

PY - 2024/8

Y1 - 2024/8

N2 - In this paper, the first family of conforming finite element divdiv complexes on cuboid meshes is constructed. The complex exhibits exactness on a contractible domain in the sense that the kernel space of each successive discrete map is the range of the previous one. This allows for algebraic structure-preserving finite element discretization of both the biharmonic equation and the linearized Einstein–Bianchi system. The convergence of optimal order is established and validated through numerical examples.

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KW - 35B45

KW - 65N12

KW - 65N15

KW - 65N30

KW - Primary 65M60

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JF - Numerische Mathematik

IS - 4

ER -

A family of conforming finite element divdiv complexes on cuboid meshes

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