An Lp spaces-based mixed virtual element method for the two-dimensional Navier–Stokes equations

DOI10.1142/S0218202521500664zbMath1478.65125OpenAlexW3210729141MaRDI QIDQ5024420

Filánder A. Sequeira, Gabriel N. Gatica

Publication date: 31 January 2022

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202521500664

zbMATH Keywords

Banach spaceshigh-order approximationsNavier-Stokes problemmixed virtual element methodpseudostress-velocity formulation

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) 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) Finite element methods applied to problems in fluid mechanics (76M10) Numerical methods for partial differential equations, boundary value problems (65N99)

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Cites Work

• Unnamed Item
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• \(H(\mathrm{div})\) and \(H(\mathbf{curl})\)-conforming virtual element methods
• A \(\mathbb {RT}_k-\mathbf P_k\) approximation for linear elasticity yielding a broken \(H(\mathrm{div})\) convergent postprocessed stress
• Dual-mixed finite element methods for the stationary Boussinesq problem
• A mixed virtual element method for a nonlinear Brinkman model of porous media flow
• Theory and practice of finite elements.
• A divergence free weak virtual element method for the Stokes-Darcy problem on general meshes
• The nonconforming virtual element method for the Darcy-Stokes problem
• A Banach spaces-based analysis of a new mixed-primal finite element method for a coupled flow-transport problem
• A virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problem
• \(p\)- and \(hp\)-virtual elements for the Stokes problem
• Some aspects on the computational implementation of diverse terms arising in mixed virtual element formulations
• A posteriori error analysis of a mixed virtual element method for a nonlinear Brinkman model of porous media flow
• Banach spaces-based analysis of a fully-mixed finite element method for the steady-state model of fluidized beds
• A virtual element method for the coupled Stokes-Darcy problem with the Beaver-Joseph-Saffman interface condition
• A nonconforming virtual element method for the Stokes problem on general meshes
• The Stokes complex for virtual elements with application to Navier-Stokes flows
• A divergence free weak virtual element method for the Stokes problem on polytopal meshes
• A virtual element method for elastic and inelastic problems on polytope meshes
• The nonconforming virtual element method for the Navier-Stokes equations
• An Augmented Mixed Finite Element Method for the Navier--Stokes Equations with Variable Viscosity
• Analysis of an augmented mixed-primal formulation for the stationary Boussinesq problem
• Mixed virtual element methods for general second order elliptic problems on polygonal meshes
• A Simple Introduction to the Mixed Finite Element Method
• Basic principles of mixed Virtual Element Methods
• Analysis of an augmented mixed-FEM for the Navier-Stokes problem
• Divergence free virtual elements for the stokes problem on polygonal meshes
• Potential Space Estimates for Green Potentials in Convex Domains
• A Banach spaces-based analysis of a new fully-mixed finite element method for the Boussinesq problem
• A Mixed Virtual Element Method for The Boussinesq Problem on Polygonal meshes
• Finite Element Methods for Navier-Stokes Equations
• Generalized Inf-Sup Conditions for Chebyshev Spectral Approximation of the Stokes Problem
• A Mixed Virtual Element Method for Quasi-Newtonian Stokes Flows
• A mixed virtual element method for the Navier–Stokes equations
• Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes
• A mixed virtual element method for the pseudostress–velocity formulation of the Stokes problem
• The Stokes complex for Virtual Elements in three dimensions
• The Divergence-Free Nonconforming Virtual Element for the Stokes Problem
• A mixed virtual element method for the Brinkman problem
• An augmented stress‐based mixed finite element method for the steady state Navier‐Stokes equations with nonlinear viscosity
• A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
• The NonConforming Virtual Element Method for the Stokes Equations
• Virtual element method for quasilinear elliptic problems