A divergence-free reconstruction of the nonconforming virtual element method for the Stokes problem
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Publication:2020931
DOI10.1016/j.cma.2020.113351zbMath1506.76092OpenAlexW3082484845MaRDI QIDQ2020931
Publication date: 26 April 2021
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2020.113351
independenceStokes problemoptimal error estimatesdivergence-freepolygonal meshesnonconforming virtual element method
Stokes and related (Oseen, etc.) flows (76D07) 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 (11)
Analysis and computation of a pressure-robust method for the rotation form of the incompressible Navier-Stokes equations with high-order finite elements ⋮ A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes ⋮ Pressure-independent velocity error estimates for (Navier-)Stokes nonconforming virtual element discretization with divergence free ⋮ The virtual element method ⋮ A pressure-robust virtual element method for the Navier-Stokes problem on polygonal mesh ⋮ The Morley-type virtual element method for the Navier-Stokes equations in stream-function form ⋮ A virtual element method for overcoming locking phenomena in Biot’s consolidation model ⋮ A pressure-robust virtual element method for the Stokes problem ⋮ A modified nonconforming virtual element with BDM-like reconstruction for the Navier-Stokes equations ⋮ Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions ⋮ An introduction to second order divergence-free VEM for fluidodynamics
Uses Software
Cites Work
- Unnamed Item
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- \(H(\mathrm{div})\) and \(H(\mathbf{curl})\)-conforming virtual element methods
- Stable finite element pair for Stokes problem and discrete Stokes complex on quadrilateral grids
- Equivalent projectors for virtual element methods
- Stokes elements on cubic meshes yielding divergence-free approximations
- \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
- On the parameter choice in grad-div stabilization for the Stokes equations
- Virtual element methods for plate bending problems
- Serendipity face and edge VEM spaces
- Grad-div stabilization and subgrid pressure models for the incompressible Navier-Stokes equations
- On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime
- On the accuracy of the rotation form in simulations of the Navier-Stokes equations
- Numerical solution of the incompressible Navier-Stokes equations with Coriolis forces based on the discretization of the total time derivative
- High-order virtual element method on polyhedral meshes
- Serendipity nodal VEM spaces
- The virtual element method for discrete fracture network simulations
- On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes
- Arbitrary order 2D virtual elements for polygonal meshes: I: Elastic problem
- Arbitrary order 2D virtual elements for polygonal meshes. II: Inelastic problem
- A virtual element method for the Cahn-Hilliard problem in mixed form
- Bricks for the mixed high-order virtual element method: projectors and differential operators
- Some basic formulations of the virtual element method (VEM) for finite deformations
- A nonconforming virtual element method for the Stokes problem on general meshes
- Virtual element approximation of 2D magnetostatic problems
- Lowest order virtual element approximation of magnetostatic problems
- The Stokes complex for virtual elements with application to Navier-Stokes flows
- The nonconforming virtual element method for the Navier-Stokes equations
- A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations
- A fully discrete virtual element scheme for the Cahn-Hilliard equation in mixed form
- Virtual Element Method for general second-order elliptic problems on polygonal meshes
- The nonconforming virtual element method
- The nonconforming virtual element method for plate bending problems
- Virtual Elements for Linear Elasticity Problems
- Stokes Complexes and the Construction of Stable Finite Elements with Pointwise Mass Conservation
- Conforming and divergence-free Stokes elements on general triangular meshes
- Basic principles of mixed Virtual Element Methods
- Divergence free virtual elements for the stokes problem on polygonal meshes
- Divergence-free finite elements on tetrahedral grids for $k\ge6$
- IsoGeometric Analysis: Stable elements for the 2D Stokes equation
- A $C^1$ Virtual Element Method for the Cahn--Hilliard Equation with Polygonal Meshes
- New Finite Element Methods in Computational Fluid Dynamics by H(div) Elements
- A Family of $Q_{k+1,k}\timesQ_{k,k+1}$ Divergence-Free Finite Elements on Rectangular Grids
- A Robust Numerical Method for Stokes Equations Based on Divergence-FreeH(div) Finite Element Methods
- Finite Element Methods for Navier-Stokes Equations
- 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
- The fully nonconforming virtual element method for biharmonic problems
- Dual Virtual Element Method for Discrete Fractures Networks
- Ill‐conditioning in the virtual element method: Stabilizations and bases
- Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes
- A new family of stable mixed finite elements for the 3D Stokes equations
- Conforming and nonconforming virtual element methods for elliptic problems
- Grad-div stablilization for Stokes equations
- BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
- Mixed Finite Element Methods and Applications
- ISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE STEADY NAVIER–STOKES EQUATIONS
- The Stokes complex for Virtual Elements in three dimensions
- The Hitchhiker's Guide to the Virtual Element Method
- A virtual element method for the Steklov eigenvalue problem
- On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows
- Virtual Element and Discontinuous Galerkin Methods
- A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
- The NonConforming Virtual Element Method for the Stokes Equations
- Finite Element Methods and Their Applications
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