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

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 element Hodge decomposition de Rham complex exterior calculus incompressible Navier-Stokes mixed 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