The Morley-type virtual element method for the Navier-Stokes equations in stream-function form

DOI10.1016/j.cma.2023.116573arXiv2212.02173MaRDI QIDQ6185145

Dibyendu Adak, David Mora, Alberth Silgado

Publication date: 29 January 2024

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.02173

zbMATH Keywords

optimal error estimates discrete Sobolev embeddings Stokes complex stream-function form nonconforming virtual elements velocity-vorticity-pressure recovery

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Error bounds for boundary value problems involving PDEs (65N15) 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)

Cites Work

Unnamed Item
$H(\mathrm{div})$ and $H(\mathbf{curl})$-conforming virtual element methods
Virtual element methods for plate bending problems
Analysis of nonconforming stream function and pressure finite element spaces for the Navier-Stokes equations
Non-conforming harmonic virtual element method: $h$- and $p$-versions
Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics
The Morley-type virtual element for plate bending problems
A hybrid high-order locking-free method for linear elasticity on general meshes
Some error analysis on virtual element methods
A hybrid high-order method for the steady incompressible Navier-Stokes problem
High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
Fully computable bounds for a staggered discontinuous Galerkin method for the Stokes equations
A divergence-free reconstruction of the nonconforming virtual element method for the Stokes problem
Morley finite element methods for the stationary quasi-geostrophic equation
Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
A $C^1$ virtual element method for the stationary quasi-geostrophic equations of the ocean
A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems
A posteriori error estimation for a $C^1$ virtual element method of Kirchhoff plates
A medius error analysis for nonconforming virtual element methods for Poisson and biharmonic equations
A hybrid high-order method for the incompressible Navier-Stokes problem robust for large irrotational body forces
Analysis and approximation of a vorticity-velocity-pressure formulation for the Oseen equations
The Stokes complex for virtual elements with application to Navier-Stokes flows
A virtual element method for the acoustic vibration problem
The nonconforming virtual element method for the Navier-Stokes equations
The nonconforming virtual element method
A $C^1$ Virtual Element Method for the Cahn--Hilliard Equation with Polygonal Meshes
Finite Element Methods for Navier-Stokes Equations
Finite Element Technique for Optimal Pressure Recovery from Stream Function Formulation of Viscous Flows
On the boundary value problem of the biharmonic operator on domains with angular corners
Numerical Computations of Viscous, Incompressible Flow Problems Using a Two-Level Finite Element Method
The fully nonconforming virtual element method for biharmonic problems
A mixed virtual element method for the Navier–Stokes equations
Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes
A note on the devising of superconvergent HDG methods for Stokes flow byM-decompositions
Conforming and nonconforming virtual element methods for elliptic problems
BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation
Bivariate spline method for numerical solution of steady state Navier-Stokes equations over polygons in stream function formulation
Nonconforming Virtual Element Method for $2m$th Order Partial Differential Equations in $\mathbb {R}^n$
Nonconforming finite element discretization for semilinear problems with trilinear nonlinearity
A nonconforming Trefftz virtual element method for the Helmholtz problem
Divergence-preserving reconstructions on polygons and a really pressure-robust virtual element method for the Stokes problem
A virtual element discretization for the time dependent Navier–Stokes equations in stream-function formulation
Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients
Conforming and nonconforming virtual element methods for a Kirchhoff plate contact problem
Conforming and nonconforming VEMs for the fourth-order reaction–subdiffusion equation: a unified framework
The Divergence-Free Nonconforming Virtual Element for the Stokes Problem
Discontinuous Galerkin finite element approximation of the two‐dimensional Navier–Stokes equations in stream‐function formulation
A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes
The NonConforming Virtual Element Method for the Stokes Equations
Conforming polygonal finite elements
Preface
A weak Galerkin finite element method for the Navier-Stokes equations
Nonconforming Virtual Elements for the Biharmonic Equation with Morley Degrees of Freedom on Polygonal Meshes
The divergence‐free nonconforming virtual element method for the <scp>Navier–Stokes</scp> problem
Stability and interpolation properties for Stokes-like virtual element spaces
A Morley-type virtual element approximation for a wind-driven ocean circulation model on polygonal meshes

This page was built for publication: The Morley-type virtual element method for the Navier-Stokes equations in stream-function form