The Abstract Hodge--Dirac Operator and Its Stable Discretization

DOI10.1137/15M1047684zbMath1353.65122arXiv1401.1576OpenAlexW3102291936MaRDI QIDQ2834566

Paul Leopardi, Ari Stern

Publication date: 23 November 2016

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

Full work available at URL: https://arxiv.org/abs/1401.1576

zbMATH Keywords

stabilityconvergencegeometric calculusClifford analysisHodge theoryHodge-Laplace operatorfinite element exterior calculusHodge-Dirac operator

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) Hodge theory in global analysis (58A14) Exterior differential systems (Cartan theory) (58A15)

Related Items (4)

An Arbitrary Order and Pointwise Divergence-Free Finite Element Scheme for the Incompressible 3D Navier–Stokes Equations ⋮ Rough metrics on manifolds and quadratic estimates ⋮ Script Geometry ⋮ First-Kind Boundary Integral Equations for the Dirac Operator in 3-Dimensional Lipschitz Domains

Uses Software

• FEniCS

Cites Work

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• A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
• An introduction to Dirac operators on manifolds
• Automated solution of differential equations by the finite element method. The FEniCS book
• Quadratic estimates and functional calculi of perturbed Dirac operators
• Aspects of Dirac operators in analysis
• Mixed finite elements in \(\mathbb{R}^3\)
• Hilbert complexes
• A new proof of the positive energy theorem.
• Discrete Poincaré lemma
• Clifford analysis: History and perspective
• Discrete Dirac operators in Clifford analysis
• Error-bounds for finite element method
• Local bounded cochain projections
• Finite elements in computational electromagnetism
• Finite element exterior calculus, homological techniques, and applications
• Finite element exterior calculus: from Hodge theory to numerical stability
• Mixed and Hybrid Finite Element Methods
• Canonical construction of finite elements
• Further results in discrete Clifford analysis
• Discrete Clifford Analysis: A Germ of Function Theory
• Finite element differential forms on cubical meshes
• Smoothed projections in finite element exterior calculus
• The index of elliptic operators on compact manifolds

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