\(p\)- and \(hp\)-virtual elements for the Stokes problem

DOI10.1007/s10444-020-09831-wzbMath1475.65187arXiv2006.10644OpenAlexW3137952889MaRDI QIDQ2027779

Lorenzo Mascotto, Alexey Chernov, Carlo Marcati

Publication date: 28 May 2021

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.10644

zbMATH Keywords

Stokes equationpolygonal meshesvirtual element methods\(p\)- and \(hp\)-Galerkin methods

Mathematics Subject Classification ID

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)

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Cites Work

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• Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem
• Analytic regularity of Stokes flow on polygonal domains in countably weighted Sobolev spaces
• The h-p version of the finite element method. I. The basic approximation results
• Mixed \(hp\) finite element methods for Stokes and non-Newtonian flow
• High-order virtual element method on polyhedral meshes
• The h, p and h-p versions of the finite element method in 1 dimension. II. The error analysis of the h- and h-p versions
• \(hp\)-finite element simulations for Stokes flow -- stable and stabilized
• A divergence free weak virtual element method for the Stokes-Darcy problem on general meshes
• Bricks for the mixed high-order virtual element method: projectors and differential operators
• Stabilized virtual element methods for the unsteady incompressible Navier-Stokes equations
• A nonconforming virtual element method for the Stokes problem on general meshes
• The Stokes complex for virtual elements with application to Navier-Stokes flows
• On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne
• Exponential convergence of the \(hp\) virtual element method in presence of corner singularities
• Exponential convergence of mixed \(hp\)-DGFEM for Stokes flow in polygons
• The nonconforming virtual element method for the Navier-Stokes equations
• An error indicator for mortar element solutions to the Stokes problem
• Divergence free virtual elements for the stokes problem on polygonal meshes
• Stabilized hp-DGFEM for Incompressible Flow
• Basic principles of hp virtual elements on quasiuniform meshes
• Analytic Regularity for the Incompressible Navier--Stokes Equations in Polygons
• The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries
• Mixedhp-DGFEM for Incompressible Flows
• Virtual element methods on meshes with small edges or faces
• Stability analysis for the virtual element method
• An H1-conforming virtual element for Darcy and Brinkman equations
• A Mixed Virtual Element Method for Quasi-Newtonian Stokes Flows
• Ill‐conditioning in the virtual element method: Stabilizations and bases
• 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
• Anisotropic Error Estimates of the Linear Virtual Element Method on Polygonal Meshes
• Mixed hp-DGFEM for incompressible flows II: Geometric edge meshes
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• Mixed Finite Element Methods and Applications
• The Stokes complex for Virtual Elements in three dimensions
• Exponential convergence of mixed hp-DGFEM for the incompressible Navier–Stokes equations in ℝ2
• The triangular spectral element method for Stokes eigenvalues
• A mixed virtual element method for the Brinkman problem
• A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
• Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftzhp-dGFEM
• The NonConforming Virtual Element Method for the Stokes Equations

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