Constructive spectral approaches for the Helmholtz decomposition of a vector field

DOI10.1016/j.apnum.2007.04.005zbMath1143.65088OpenAlexW2057871800MaRDI QIDQ932753

Michel O. Deville, Ernest Mund, Ralf Gruber, Mejdi Aza ıïez, Etienne Ahusborde

Publication date: 11 July 2008

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2007.04.005

zbMATH Keywords

eigenvalue problemHelmholtz decompositioncurl freedivergence freeprimal and dual formulationspectral elementgrad(div) operator

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows
• A remark on spurious eigenvalues in a square
• Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires. I
• A Uniformly Accurate Finite Element Method for the Reissner–Mindlin Plate
• Finite Element Methods for Navier-Stokes Equations
• Numerical Approximation of Mindlin-Reissner Plates
• Approximation of the Spectrum of Closed Operators: The Determination of Normal Modes of a Rotating Basin
• Mixed and Hybrid Finite Element Methods
• Preconditioning in H(𝑑𝑖𝑣) and applications
• High-Order Methods for Incompressible Fluid Flow
• On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form
• Sur une méthode de projection vectorielle pour la résolution des équations de Navier-Stokes
• Numerical Solution of the Navier-Stokes Equations
• Penalized approximation of the vibration frequencies of a fluid in a cavity
• A Galerkin implementation of the generalized Helmholtz decomposition for vorticity formulations