Conforming Finite Element DIVDIV Complexes and the Application for the Linearized Einstein--Bianchi System

DOI10.1137/21M1404235zbMath1490.65275arXiv2103.00088OpenAlexW3135225428MaRDI QIDQ5864681

Yizhou Liang, Rui Ma, Jun Hu

Publication date: 8 June 2022

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.00088

zbMATH Keywords

\(H(\mathrm{sym}\,\mathrm{curl})\) conforming finite elementdivdiv complexlinearized Einstein-Bianchi system

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Einstein-Maxwell equations (83C22) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Einstein equations (35Q76)

Related Items (3)

On \([H^1^{3\times 3}, [H(\text{curl})]^3\) and \(H(\text{sym Curl})\) finite elements for matrix-valued curl problems] ⋮ Finite element de Rham and Stokes complexes in three dimensions ⋮ Novel \(H(\mathrm{sym\,Curl})\)-conforming finite elements for the relaxed micromorphic sequence

Cites Work

• A family of mixed finite elements for the biharmonic equations on triangular and tetrahedral grids
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• Mixed finite elements for elasticity
• Fully discrete DPG methods for the Kirchhoff-Love plate bending model
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• Complexes from complexes
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• An ultraweak formulation of the Kirchhoff–Love plate bending model and DPG approximation
• Mixed Finite Element Methods and Applications
• Conforming discrete Gradgrad-complexes in three dimensions
• Finite elements for divdiv conforming symmetric tensors in three dimensions
• The divDiv-complex and applications to biharmonic equations
• Mixed Methods for Elastodynamics with Weak Symmetry

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