A divergence free weak virtual element method for the Stokes problem on polytopal meshes
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Publication:2420686
DOI10.1007/s10915-018-0796-5zbMath1433.76074OpenAlexW2887442002MaRDI QIDQ2420686
Publication date: 6 June 2019
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-018-0796-5
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)
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Cites Work
- Unnamed Item
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- \(H(\mathrm{div})\) and \(H(\mathbf{curl})\)-conforming virtual element methods
- A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation
- \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
- A simple preconditioner for a discontinuous Galerkin method for the Stokes problem
- Serendipity face and edge VEM spaces
- A comparison of HDG methods for Stokes flow
- Mimetic finite difference method
- Devising \(\mathbf{HDG}\) methods for Stokes flow: an overview
- A hybrid high-order locking-free method for linear elasticity on general meshes
- Some error analysis on virtual element methods
- A weak Galerkin finite element method for second-order elliptic problems
- A discontinuous skeletal method for the viscosity-dependent Stokes problem
- A nonconforming virtual element method for the Stokes problem on general meshes
- A weak Galerkin finite element method with polynomial reduction
- Convergence analysis of triangular MAC schemes for two dimensional Stokes equations
- A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations
- 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
- Conforming and divergence-free Stokes elements in three dimensions
- Divergence free virtual elements for the stokes problem on polygonal meshes
- Minimal degree $H(\mathrm {curl})$ and $H(\mathrm {div})$ conforming finite elements on polytopal meshes
- Divergence-free finite elements on tetrahedral grids for $k\ge6$
- Weak Galerkin Finite Element Methods on Polytopal Meshes
- New Finite Element Methods in Computational Fluid Dynamics by H(div) Elements
- Finite Element Methods for Navier-Stokes Equations
- Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials
- Poincaré--Friedrichs Inequalities for Piecewise H1 Functions
- Virtual element methods on meshes with small edges or faces
- An H1-conforming virtual element for Darcy and Brinkman equations
- Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes
- A Robust Finite Element Method for Darcy--Stokes Flow
- Korn's inequalities for piecewise $H^1$ vector fields
- BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
- Mixed Finite Element Methods and Applications
- Polygonal finite elements for incompressible fluid flow
- Divergence-free Reconstruction Operators for Pressure-Robust Stokes Discretizations with Continuous Pressure Finite Elements
- On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows
- A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
- Divergence-conforming HDG methods for Stokes flows
- An extension of the Crouzeix–Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow
- The NonConforming Virtual Element Method for the Stokes Equations
- An observation on Korn’s inequality for nonconforming finite element methods
- A weak Galerkin finite element method for the Stokes equations
