Divergence free virtual elements for the stokes problem on polygonal meshes

From MaRDI portal
Publication:2977902

DOI10.1051/m2an/2016032zbMath1398.76094arXiv1510.01655OpenAlexW2963131956MaRDI QIDQ2977902

Giuseppe Vacca, Lourenco Beirão da Veiga, Carlo Lovadina

Publication date: 20 April 2017

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.01655




Related Items

Virtual element method for semilinear hyperbolic problems on polygonal meshesA C0 virtual element method for the biharmonic eigenvalue problemVirtual element method for nonlinear convection–diffusion–reaction equation on polygonal meshesA hybrid high-order method for creeping flows of non-Newtonian fluidsBasic convergence theory for the network element methodA virtual element discretization for the time dependent Navier–Stokes equations in stream-function formulationThe interior penalty virtual element method for the biharmonic problemDivergence Free VEM for the Stokes Problem with No Internal Degrees of FreedomVIRTUAL ELEMENT APPROXIMATIONS FOR TWO SPECIES MODEL OF THE ADVECTION-DIFFUSION-REACTION IN POROELASTIC MEDIAThe Scott-Vogelius finite elements revisitedRobust and scalable adaptive BDDC preconditioners for virtual element discretizations of elliptic partial differential equations in mixed formA new local projection stabilization virtual element method for the Oseen problem on polygonal meshesAn arbitrary-order fully discrete Stokes complex on general polyhedral meshesThe virtual element methodThe interior penalty virtual element method for the fourth-order elliptic hemivariational inequalityVirtual element method for elliptic bulk‐surface PDEs in three space dimensionsThe nonconforming locking-free virtual element method for the Biot's consolidation model in poroelasticity\( \boldsymbol{H}^1\)-conforming virtual element method for the Laplacian eigenvalue problem in mixed formA pressure-robust virtual element method for the Navier-Stokes problem on polygonal meshAdaptive and frugal FETI-DP for virtual elementsThe divergence‐free nonconforming virtual element method for the <scp>Navier–Stokes</scp> problemA pressure‐robust weak Galerkin finite element method for <scp>Navier–Stokes</scp> equationsA stabilized divergence-free virtual element scheme for the nematic liquid crystal flowsVirtual element method for the modified transmission eigenvalue problem in inverse scattering theoryAdaptive virtual element method for optimal control problem governed by Stokes equationsStability analysis for the virtual element methodStability and interpolation properties for Stokes-like virtual element spacesVariable-time-step BDF2 nonconforming VEM for coupled Ginzburg-Landau equationsThe virtual element method for a 2D incompressible MHD systemThe Bulk-Surface Virtual Element Method for Reaction-Diffusion PDEs: Analysis and ApplicationsA conforming virtual element method based on unfitted meshes for the elliptic interface problemThe virtual element method with interior penalty for the fourth-order singular perturbation problemA new class of stabilized virtual element methods for the time-dependent Oseen equationsTheoretical analysis and construction of numerical method for solving the Navier-Stokes equations in rotation form with corner singularityA nonconforming immersed virtual element method for elliptic interface problemsVirtual element method for nonlinear Sobolev equation on polygonal meshesThe Hermite-type virtual element method with interior penalty for the fourth-order elliptic problemThe role of stabilization in the virtual element method: a surveyAn H1-conforming virtual element for Darcy and Brinkman equationsReduced basis stabilization and post-processing for the virtual element methodNonconforming virtual element methods for the fourth-order variational inequalities of the first kindA Morley-type virtual element approximation for a wind-driven ocean circulation model on polygonal meshesOptimal error estimates of coupled and divergence-free virtual element methods for the Poisson-Nernst-Planck/Navier-Stokes equations and applications in electrochemical systemsThe virtual element method for the 3D resistive magnetohydrodynamic modelAn extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flowsVirtual element method for linear elastic clamped plate modelAnalysis of divergence free conforming virtual elements for the Brinkman problemFETI-DP for the Three Dimensional Virtual Element MethodThe nonconforming virtual element method for Oseen’s equation using a stream-function formulationLeast-squares virtual element method for Stokes problems on polygonal meshesOn stabilized equal-order virtual element methods for the Navier-Stokes equations on polygonal meshesA posteriori error analysis and adaptivity for a VEM discretization of the Navier-Stokes equationsBDDC Preconditioners for Virtual Element Approximations of the Three-Dimensional Stokes EquationsA family of three-dimensional virtual elements for Hellinger-Reissner elasticity problemsDissipative nonconforming virtual element method for the fourth order nonlinear extended Fisher-Kolmogorov equationNumerical solution of the Biot/elasticity interface problem using virtual element methodsA Mixed Virtual Element Method for Quasi-Newtonian Stokes FlowsThe fully nonconforming virtual element method for biharmonic problemsConservative Conforming and Nonconforming Vems for Fourth Order Nonlinear Schrödinger Equations with Trapped TermUnconditional Error Analysis of VEMs for a Generalized Nonlinear Schrödinger EquationShape optimization with virtual element methodA mixed virtual element method for nearly incompressible linear elasticity equationsA fully-discrete virtual element method for the nonstationary Boussinesq equations in stream-function formGeneralized weak Galerkin methods for Stokes equationsA fully discrete virtual element scheme for the Cahn-Hilliard equation in mixed formPolynomial preserving virtual elements with curved edgesIll‐conditioning in the virtual element method: Stabilizations and basesA mixed virtual element method for the Navier–Stokes equationsA virtual element method for the transmission eigenvalue problemVirtual Elements for the Navier--Stokes Problem on Polygonal MeshesThe Mixed Virtual Element Method for the Richards EquationEquilibrium analysis of an immersed rigid leaflet by the virtual element methodThe curl–curl conforming virtual element method for the quad-curl problemA Divergence-Free Stabilized Finite Element Method for the Evolutionary Navier--Stokes EquationsA weak Galerkin finite element method for the Navier-Stokes equationsVirtual elements for a shear-deflection formulation of Reissner–Mindlin platesA Family of Three-Dimensional Virtual Elements with Applications to MagnetostaticsUnnamed ItemOn the locking-free three-field virtual element methods for Biot’s consolidation model in poroelasticityThe Stokes complex for Virtual Elements in three dimensionsConvergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshesVirtual Element approximations of the Vector Potential Formulation of Magnetostatic problemsA nonconforming Trefftz virtual element method for the Helmholtz problemThe Virtual Element Method with curved edgesThe nonconforming Virtual Element Method for eigenvalue problemsDivergence-free Scott--Vogelius Elements on Curved DomainsA dual hybrid virtual element method for plane elasticity problemsOn the Coupling of VEM and BEM in Two and Three DimensionsThe Divergence-Free Nonconforming Virtual Element for the Stokes ProblemThe Stokes complex: A review of exactly divergence–free finite element pairs for incompressible flowsPiecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any DimensionsThe NonConforming Virtual Element Method for the Stokes EquationsA review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equationsAn Lp spaces-based mixed virtual element method for the two-dimensional Navier–Stokes equationsVorticity-stabilized virtual elements for the Oseen equationPrinciples of a network element methodA mixed virtual element method for a pseudostress-based formulation of linear elasticityA divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshesA virtual element method for the acoustic vibration problemVirtual element methods for nonlocal parabolic problems on general type of meshesA virtual element method for the two-phase flow of immiscible fluids in porous mediaA virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problemAn advection-robust hybrid high-order method for the Oseen problemPressure-independent velocity error estimates for (Navier-)Stokes nonconforming virtual element discretization with divergence freeNon-conforming harmonic virtual element method: \(h\)- and \(p\)-versionsThe nonconforming virtual element method for the Navier-Stokes equationsA hybrid high-order method for the Sobolev equationUnconditionally energy stable \(C^0\)-virtual element scheme for solving generalized Swift-Hohenberg equationArbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshesStabilization of the nonconforming virtual element methodA \(C^1\) virtual element method for the stationary quasi-geostrophic equations of the oceanVirtual element methods for hyperbolic problems on polygonal meshesOn the virtual element method for topology optimization on polygonal meshes: a numerical studyHigh-order virtual element method on polyhedral meshesMimetic finite difference methods for Hamiltonian wave equations in 2DBDDC preconditioners for divergence free virtual element discretizations of the Stokes equationsThe nonconforming virtual element method for semilinear elliptic problemsA robust and mass conservative virtual element method for linear three-field poroelasticityA formal construction of a divergence-free basis in the nonconforming virtual element method for the Stokes problemConforming virtual element approximations of the two-dimensional Stokes problemA unified analysis of fully mixed virtual element method for wormhole propagation arising in the petroleum engineeringVirtual element method on polyhedral meshes for bi-harmonic eigenvalues problemsOn nonconvex meshes for elastodynamics using virtual element methods with explicit time integrationVirtual element for the buckling problem of Kirchhoff-Love platesA three-dimensional Hellinger-Reissner virtual element method for linear elasticity problemsExponential convergence of the \(hp\) virtual element method in presence of corner singularitiesA divergence free weak virtual element method for the Stokes problem on polytopal meshesA virtual element method for the Laplacian eigenvalue problem in mixed formVirtual element method for a nonlocal elliptic problem of Kirchhoff type on polygonal meshesRelationship between the vertex-centered linearity-preserving scheme and the lowest-order virtual element method for diffusion problems on star-shaped polygonsMixed virtual element methods for elastodynamics with weak symmetryA posteriori error analysis of a mixed virtual element method for a nonlinear Brinkman model of porous media flowA low-order locking-free virtual element for linear elasticity problemsBDDC and FETI-DP for the virtual element methodA mixed virtual element method for the vibration problem of clamped Kirchhoff plateA new projection-based stabilized virtual element method for the Stokes problemParallel solvers for virtual element discretizations of elliptic equations in mixed formThe nonconforming virtual element method for a stationary Stokes hemivariational inequality with slip boundary conditionExploring high-order three dimensional virtual elements: bases and stabilizationsConforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: a unified frameworkA pressure-robust virtual element method for the Stokes problemEnrichment of the nonconforming virtual element method with singular functionsAn adaptive virtual element method for incompressible flowA hybrid high-order method for the steady incompressible Navier-Stokes problemOn the application of polygonal finite element method for Stokes flow -- a comparison between equal order and different order approximationA family of virtual element methods for plane elasticity problems based on the Hellinger-Reissner principleA hybrid high-order discretisation of the Brinkman problem robust in the Darcy and Stokes limitsA projection-based stabilized virtual element method for the unsteady incompressible Brinkman equationsBricks for the mixed high-order virtual element method: projectors and differential operatorsA local projection stabilization virtual element method for convection-diffusion-reaction equationBulk-surface virtual element method for systems of PDEs in two-space dimensionsSerendipity virtual elements for general elliptic equations in three dimensionsVirtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulationA virtual element method for stochastic Stokes equationsA posteriori error estimates for the virtual element method for the Stokes problemStabilized virtual element methods for the unsteady incompressible Navier-Stokes equationsThe nonconforming virtual element method for the Darcy-Stokes problemVirtual element method for semilinear elliptic problems on polygonal meshesA divergence-free reconstruction of the nonconforming virtual element method for the Stokes problemParallel block preconditioners for three-dimensional virtual element discretizations of saddle-point problemsA virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problemVirtual element methods for the three-field formulation of time-dependent linear poroelasticity\(p\)- and \(hp\)-virtual elements for the Stokes problemA virtual element method for the coupled Stokes-Darcy problem with the Beaver-Joseph-Saffman interface conditionA mixed virtual element method for a nonlinear Brinkman model of porous media flowA modified nonconforming virtual element with BDM-like reconstruction for the Navier-Stokes equationsOn the \({H}^1\) conforming virtual element method for time dependent Stokes equationA lowest-order virtual element method for the Helmholtz transmission eigenvalue problemA priori error analysis for a mixed VEM discretization of the spectral problem for the Laplacian operatorA virtual element method for the Steklov eigenvalue problem allowing small edgesStability analysis of polytopic discontinuous Galerkin approximations of the Stokes problem with applications to fluid-structure interaction problemsLowest order virtual element approximations for transient Stokes problem on polygonal meshesTwo robust virtual element methods for the Brinkman equationsA hybrid high-order method for the incompressible Navier-Stokes problem robust for large irrotational body forcesA nonconforming virtual element method for the Stokes problem on general meshesA stress/displacement virtual element method for plane elasticity problemsVirtual element approximation of 2D magnetostatic problemsA hybrid high-order method for the incompressible Navier-Stokes equations based on Temam's deviceThe nonconforming virtual element method for elasticity problemsA posteriori error estimation and adaptivity in \textit{hp} virtual elementsLowest-order virtual element methods for linear elasticity problemsHigh order VEM on curved domainsWeakly imposed Dirichlet boundary conditions for 2D and 3D virtual elementsError estimates for a vorticity-based velocity-stress formulation of the Stokes eigenvalue problemThe Stokes complex for virtual elements with application to Navier-Stokes flowsUnconditional error analysis of a linearized BDF2 virtual element method for nonlinear Ginzburg-Landau equation with variable time stepVirtual element methods for three-dimensional Hellinger-Reissner elastostatic problemsOn the implementation of virtual element method for nonlinear problems over polygonal meshesDiscrete Hessian complexes in three dimensionsSome virtual element methods for infinitesimal elasticity problemsAn introduction to second order divergence-free VEM for fluidodynamicsA virtual marriage à la mode: some recent results on the coupling of VEM and BEMVirtual element methods for a stream-function formulation of the Oseen equationsThe virtual element method for the coupled system of magneto-hydrodynamicsArtificial compressibility methods for the incompressible Navier-Stokes equations using lowest-order face-based schemes on polytopal meshes


Uses Software