Crouzeix-Raviart triangular elements are inf-sup stable

DOI10.1090/mcom/3742zbMath1496.65211arXiv2105.14987OpenAlexW3170203178MaRDI QIDQ5097368

Carsten Carstensen, Stefan A. Sauter

Publication date: 23 August 2022

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.14987

zbMATH Keywords

Stokes problemnonconforminginf-sup stabilityodd degreeCrouzeix-Raviart\(p=3\)arbitrary \(p\)

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) 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) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items (3)

The inf-sup constant for \textit{hp}-Crouzeix-Raviart triangular elements ⋮ A vorticity-based mixed formulation for the unsteady Brinkman-Forchheimer equations ⋮ On the inf-sup stability of Crouzeix-Raviart Stokes elements in 3D

Cites Work

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• Gauss-Legendre elements: a stable, higher order non-conforming finite element family
• A right-inverse for divergence operator in spaces of piecewise polynomials. Application to the p-version of the finite element method
• Critical functions and inf-sup stability of Crouzeix-Raviart elements
• Crouzeix-Velte decompositions for higher-order finite elements
• Analysis of Mixed Finite Element Methods for the Stokes Problem: A Unified Approach
• Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements
• A non-conforming piecewise quadratic finite element on triangles
• Stability of Finite Elements under Divergence Constraints
• Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials
• Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
• Nonconforming Finite Elements for the Stokes Problem
• The Fundamental Theorem of Linear Algebra
• The Scott-Vogelius finite elements revisited
• Finite Element Methods for Maxwell's Equations
• Finite Elements I
• Discrete and conforming smooth de Rham complexes in three dimensions
• A family of Crouzeix–Raviart finite elements in 3D
• The Mathematical Theory of Finite Element Methods
• A Recurring Theorem on Determinants
• Stable nonconforming methods for the Stokes problem.
• Intrinsic finite element methods for the computation of fluxes for Poisson's equation

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