Continuity Properties of the Inf-Sup Constant for the Divergence

DOI10.1137/15M1044989zbMath1339.35230arXiv1510.03978MaRDI QIDQ2798648

Monique Dauge, Christine Bernardi, Martin Costabel, Vivette Girault

Publication date: 13 April 2016

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

Full work available at URL: https://arxiv.org/abs/1510.03978

zbMATH Keywords

inf-sup conditionLBB constant

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (11)

Mixed Aggregated Finite Element Methods for the Unfitted Discretization of the Stokes Problem ⋮ Stability for Finite Element Discretization of Some Inverse Parameter Problems from Internal Data: Application to Elastography ⋮ Analysis of divergence free conforming virtual elements for the Brinkman problem ⋮ Shape sensitivity analysis for a microchannel cooling system ⋮ A Posteriori Error Analysis of the inf-sup Constant for the Divergence ⋮ Inf-sup stability of geometrically unfitted Stokes finite elements ⋮ Analysis of the shifted boundary method for the Stokes problem ⋮ Rayleigh–Ritz approximation of the inf-sup constant for the divergence ⋮ Computation of the LBB Constant for the Stokes Equation with a Least-Squares Finite Element Method ⋮ Divergence-free Scott--Vogelius Elements on Curved Domains ⋮ Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions

Uses Software

• FreeFem++

Cites Work

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• On the domain dependence of the inf-sup and related constants via conformal mapping
• Finite element approximation of the Navier-Stokes equations
• Solutions of the divergence operator on John domains
• On inequalities of Korn, Friedrichs and Babuska-Aziz
• A numerical solution of the Navier-Stokes equations using the finite element technique
• Spectral study of a self-adjoint operator on \(L^ 2(\Omega)\) related with a Poincaré type constant
• On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne
• An introduction to Navier-Stokes equation and oceanography.
• A quasi-local interpolation operator preserving the discrete divergence
• Error estimates for a mixed finite element approximation of the Stokes equations
• Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• UNIFORM INF–SUP CONDITIONS FOR THE SPECTRAL DISCRETIZATION OF THE STOKES PROBLEM
• Thepandh-pVersions of the Finite Element Method, Basic Principles and Properties
• On the domain geometry dependence of the LBB condition
• Finite elements on degenerate meshes: inverse-type inequalities and applications
• New development in freefem++
• The inf‐sup constant for the divergence on corner domains
• Inverse-type estimates on $hp$-finite element spaces and applications
• The Mathematical Theory of Finite Element Methods
• Iterative Stokes solvers in the harmonic Velte subspace

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