An Arbitrary Order and Pointwise Divergence-Free Finite Element Scheme for the Incompressible 3D Navier–Stokes Equations

DOI10.1137/21M1443686MaRDI QIDQ5889030

Unnamed Author

Publication date: 26 April 2023

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

Full work available at URL: https://arxiv.org/abs/2106.05146

zbMATH Keywords

finite elementHodge decompositionde Rham complexexterior calculusincompressible Navier-Stokesmixed element

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Finite element methods applied to problems in fluid mechanics (76M10)

Uses Software

• FEniCS

Cites Work

• Unnamed Item
• Automated solution of differential equations by the finite element method. The FEniCS book
• Vorticity-velocity-pressure and stream function-vorticity formulations for the Stokes problem.
• Helicity-conservative finite element discretization for incompressible MHD systems
• Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem
• Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier-Stokes equations
• Analysis and approximation of a vorticity-velocity-pressure formulation for the Oseen equations
• Convergence analysis of triangular MAC schemes for two dimensional Stokes equations
• Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods
• Spectral element discretization of the vorticity,velocity and pressure formulation of the Navier-Stokes problem
• The Abstract Hodge--Dirac Operator and Its Stable Discretization
• Finite element exterior calculus with lower-order terms
• MIXED FINITE ELEMENT APPROXIMATION OF THE VECTOR LAPLACIAN WITH DIRICHLET BOUNDARY CONDITIONS
• Finite element exterior calculus: from Hodge theory to numerical stability
• Finite Element Methods for Navier-Stokes Equations
• Exact fully 3D Navier–Stokes solutions for benchmarking
• On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond
• Discrete and conforming smooth de Rham complexes in three dimensions
• On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows

This page was built for publication: An Arbitrary Order and Pointwise Divergence-Free Finite Element Scheme for the Incompressible 3D Navier–Stokes Equations