A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem
From MaRDI portal
Publication:2136225
DOI10.3934/jcd.2021020zbMath1492.65324arXiv2112.13292OpenAlexW4250635476MaRDI QIDQ2136225
Gianmarco Manzini, Annamaria Mazzia
Publication date: 10 May 2022
Published in: Journal of Computational Dynamics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.13292
PDEs in connection with fluid mechanics (35Q35) Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) 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) A priori estimates in context of PDEs (35B45) Finite element methods applied to problems in fluid mechanics (76M10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)
Related Items (4)
Preface. Special issue on structural dynamical systems ⋮ Conforming virtual element approximations of the two-dimensional Stokes problem ⋮ The nonconforming virtual element method for Oseen’s equation using a stream-function formulation ⋮ Robust weak Galerkin finite element solvers for Stokes flow based on a lifting operator
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- \(H(\mathrm{div})\) and \(H(\mathbf{curl})\)-conforming virtual element methods
- Equivalent projectors for virtual element methods
- Virtual element methods for plate bending problems
- Finite element approximation of the Navier-Stokes equations
- Mimetic finite difference method
- Mimetic finite difference method for the Stokes problem on polygonal meshes
- Extended finite element method on polygonal and quadtree meshes
- A new discretization methodology for diffusion problems on generalized polyhedral meshes
- Sedimentation of inertialess particles in Stokes flows
- Serendipity nodal VEM spaces
- The virtual element method for discrete fracture network simulations
- A posteriori error estimates for the virtual element method
- A virtual element method for contact
- Discontinuous skeletal gradient discretisation methods on polytopal meshes
- Application of homogenization theory related to Stokes flow in porous media.
- The virtual element method for eigenvalue problems with potential terms on polytopic meshes.
- SUPG stabilization for the nonconforming virtual element method for advection-diffusion-reaction equations
- \(p\)- and \(hp\)-virtual elements for the Stokes problem
- Extended virtual element method for the Laplace problem with singularities and discontinuities
- The conforming virtual element method for polyharmonic problems
- The \(p\)- and \(hp\)-versions of the virtual element method for elliptic eigenvalue problems
- A posteriori error estimation and adaptivity in \textit{hp} virtual elements
- The Stokes complex for virtual elements with application to Navier-Stokes flows
- Towards effective flow simulations in realistic discrete fracture networks
- The virtual element method for underground flow simulations in fractured media
- A virtual element method for elastic and inelastic problems on polytope meshes
- The mimetic finite difference method for elliptic problems
- Virtual Element Method for general second-order elliptic problems on polygonal meshes
- Mixed virtual element methods for general second order elliptic problems on polygonal meshes
- A plane wave virtual element method for the Helmholtz problem
- The nonconforming virtual element method
- The nonconforming virtual element method for plate bending problems
- Virtual Elements for Linear Elasticity Problems
- Basic principles of mixed Virtual Element Methods
- Hourglass stabilization and the virtual element method
- Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods
- Divergence free virtual elements for the stokes problem on polygonal meshes
- Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral Meshes
- A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles
- Basic principles of hp virtual elements on quasiuniform meshes
- Rational Bases and Generalized Barycentrics
- Virtual element methods for parabolic problems on polygonal meshes
- Polygonal finite elements for topology optimization: A unifying paradigm
- Mixed finite element methods for incompressible flow: Stationary Stokes equations
- Convergence Analysis of the Mimetic Finite Difference Method for Elliptic Problems
- Finite Element Methods for Navier-Stokes Equations
- Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
- New mixed finite element method on polygonal and polyhedral meshes
- The fully nonconforming virtual element method for biharmonic problems
- Ill‐conditioning in the virtual element method: Stabilizations and bases
- Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes
- Conforming and nonconforming virtual element methods for elliptic problems
- BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
- Mixed Finite Element Methods and Applications
- The Stokes complex for Virtual Elements in three dimensions
- The Hitchhiker's Guide to the Virtual Element Method
- New perspectives on polygonal and polyhedral finite element methods
- The nonconforming Virtual Element Method for eigenvalue problems
- Residuala posteriorierror estimation for the Virtual Element Method for elliptic problems
- A virtual element method for the Steklov eigenvalue problem
- A Parallel Solver for Large Scale DFN Flow Simulations
- CONVERGENCE OF MIMETIC FINITE DIFFERENCE METHOD FOR DIFFUSION PROBLEMS ON POLYHEDRAL MESHES WITH CURVED FACES
- A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
- A virtual element method with arbitrary regularity
- The NonConforming Virtual Element Method for the Stokes Equations
- Conforming polygonal finite elements
- A Posteriori Error Estimate for a PDE-Constrained Optimization Formulation for the Flow in DFNs
- A tensor artificial viscosity using a mimetic finite differential algorithm
This page was built for publication: A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem
