Divergence free virtual elements for the Stokes problem on polygonal meshes

LB da Veiga, C Lovadina, G Vacca - … : Mathematical Modelling and …, 2017 - esaim-m2an.org
In the present paper we develop a new family of Virtual Elements for the Stokes problem on
polygonal meshes. By a proper choice of the Virtual space of velocities and the associated …

On conservation laws of Navier–Stokes Galerkin discretizations

S Charnyi, T Heister, MA Olshanskii… - Journal of Computational …, 2017 - Elsevier
We study conservation properties of Galerkin methods for the incompressible Navier–Stokes
equations, without the divergence constraint strongly enforced. In typical discretizations such …

[图书][B] Iterative methods for linear systems: theory and applications

Systems of linear algebraic equations are ubiquitous in mathematical modeling and
scientific computing, and iterative methods are indispensable for the numerical treatment of …

Robust arbitrary order mixed finite element methods for the incompressible Stokes equations with pressure independent velocity errors

A Linke, G Matthies, L Tobiska - ESAIM: Mathematical Modelling …, 2016 - esaim-m2an.org
Standard mixed finite element methods for the incompressible Navier–Stokes equations that
relax the divergence constraint are not robust against large irrotational forces in the …

Divergence-free reconstruction operators for pressure-robust Stokes discretizations with continuous pressure finite elements

PL Lederer, A Linke, C Merdon, J Schöberl - SIAM Journal on Numerical …, 2017 - SIAM
Classical inf-sup stable mixed finite elements for the incompressible (Navier--) Stokes
equations are not pressure-robust, ie, their velocity errors depend on the continuous …

A stabilizer-free, pressure-robust, and superconvergence weak Galerkin finite element method for the Stokes equations on polytopal mesh

L Mu, X Ye, S Zhang - SIAM Journal on Scientific Computing, 2021 - SIAM
In this paper, we propose a new stabilizer-free and pressure-robust weak Galerkin finite
element method for the Stokes equations with superconvergence on polytopal mesh in the …

The divergence-free nonconforming virtual element for the Stokes problem

J Zhao, B Zhang, S Mao, S Chen - SIAM Journal on Numerical Analysis, 2019 - SIAM
We present the divergence-free nonconforming virtual element method for the Stokes
problems. We first construct a nonconforming virtual element with continuous normal …

[PDF][PDF] The Scott-Vogelius finite elements revisited

J Guzmán, R Scott - arXiv preprint arXiv:1705.00020, 2017 - arxiv.org
arXiv:1705.00020v1 [math.NA] 28 Apr 2017 Page 1 THE SCOTT-VOGELIUS FINITE
ELEMENTS REVISITED JOHNNY GUZMÁN† AND L. RIDGWAY SCOTT‡ Abstract. We prove …

A pressure-robust virtual element method for the Stokes problem

G Wang, L Mu, Y Wang, Y He - Computer Methods in Applied Mechanics …, 2021 - Elsevier
In this paper, we introduce a pressure-robust virtual element method for the Stokes problem
on convex polygonal meshes. The method is based on the lowest order virtual element, in …

Inf-sup stable finite elements on barycentric refinements producing divergence--free approximations in arbitrary dimensions

J Guzmán, M Neilan - SIAM Journal on Numerical Analysis, 2018 - SIAM
We construct several stable finite element pairs for the Stokes problem on barycentric
refinements in arbitrary dimensions. A key feature of the spaces is that the divergence maps …