A virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problem

DOI10.1016/j.cma.2021.113753zbMath1506.76089arXiv2006.14775OpenAlexW3038060209MaRDI QIDQ2021909

Felipe Lepe, Gonzalo Rivera

Publication date: 27 April 2021

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.14775

zbMATH Keywords

error estimatesspectral problemsvirtual element methodStokes eigenvalue problem

Mathematics Subject Classification ID

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) Finite element methods applied to problems in fluid mechanics (76M10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (14)

A lowest-order free-stabilization virtual element method for the Laplacian eigenvalue problem ⋮ Virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media ⋮ Conforming virtual element approximations of the two-dimensional Stokes problem ⋮ \( \boldsymbol{H}^1\)-conforming virtual element method for the Laplacian eigenvalue problem in mixed form ⋮ A virtual element method for the elasticity spectral problem allowing for small edges ⋮ Discontinuous Galerkin methods for the acoustic vibration problem ⋮ Spectral Analysis of a Mixed Method for Linear Elasticity ⋮ VEM discretization allowing small edges for the reaction–convection–diffusion equation: source and spectral problems ⋮ A posteriori virtual element method for the acoustic vibration problem ⋮ A numerical implementation for the high-order 2D virtual element method in MATLAB ⋮ A \(C^1-C^0\) conforming virtual element discretization for the transmission eigenvalue problem ⋮ Error estimates for a vorticity-based velocity-stress formulation of the Stokes eigenvalue problem ⋮ Mixed Methods for the Velocity-Pressure-Pseudostress Formulation of the Stokes Eigenvalue Problem ⋮ An Lp spaces-based mixed virtual element method for the two-dimensional Navier–Stokes equations

Cites Work

• Unnamed Item
• Analysis of a velocity-pressure-pseudostress formulation for the stationary Stokes equations
• A mixed virtual element method for a nonlinear Brinkman model of porous media flow
• A divergence free weak virtual element method for the Stokes-Darcy problem on general meshes
• Stabilized virtual element methods for the unsteady incompressible Navier-Stokes equations
• The Stokes complex for virtual elements with application to Navier-Stokes flows
• A virtual element method for the acoustic vibration problem
• A divergence free weak virtual element method for the Stokes problem on polytopal meshes
• Finite Element Spectral Analysis for the Mixed Formulation of the Elasticity Equations
• Basic principles of mixed Virtual Element Methods
• Divergence free virtual elements for the stokes problem on polygonal meshes
• Finite elements in computational electromagnetism
• Mixed finite element methods for incompressible flow: Stationary Stokes equations
• On spectral approximation. Part 1. The problem of convergence
• On spectral approximation. Part 2. Error estimates for the Galerkin method
• Pseudostress-Based Mixed Finite Element Methods for the Stokes Problem in ℝⁿwith Dirichlet Boundary Conditions. I: A Priori Error Analysis
• A mixed virtual element method for the Navier–Stokes equations
• A mixed virtual element method for the pseudostress–velocity formulation of the Stokes problem
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• The Stokes complex for Virtual Elements in three dimensions
• Symmetric and Nonsymmetric Discontinuous Galerkin Methods for a Pseudostress Formulation of the Stokes Spectral Problem
• A finite element analysis of a pseudostress formulation for the Stokes eigenvalue problem
• A virtual element method for the Steklov eigenvalue problem
• A mixed virtual element method for the Brinkman problem
• A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
• A posteriori estimates for the Stokes eigenvalue problem
• The NonConforming Virtual Element Method for the Stokes Equations

This page was built for publication: A virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problem