A review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equations

DOI10.1142/S0218202521500627zbMath1478.65110arXiv2104.03402OpenAlexW3208855670WikidataQ114072930 ScholiaQ114072930MaRDI QIDQ5024416

Gianmarco Manzini, Paola Francesca Antonietti, Marco Verani, Simone Scacchi

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://arxiv.org/abs/2104.03402

zbMATH Keywords

virtual element methodsarbitrarily regular conforming approximation spacessecond- and higher-order elliptic PDEs

Mathematics Subject Classification ID

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) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (13)

\({H^m}\)-Conforming Virtual Elements in Arbitrary Dimension ⋮ The virtual element method for a 2D incompressible MHD system ⋮ Parallel block preconditioners for virtual element discretizations of the time-dependent Maxwell equations ⋮ Analysis of divergence free conforming virtual elements for the Brinkman problem ⋮ Convergence analysis for virtual element discretizations of the cardiac bidomain model ⋮ A \(C^1\)-conforming arbitrary-order two-dimensional virtual element method for the fourth-order phase-field equation ⋮ A fully-discrete virtual element method for the nonstationary Boussinesq equations in stream-function form ⋮ \(C^1 \)-VEM for some variants of the Cahn-Hilliard equation: a numerical exploration ⋮ A \(C^1\)-\(C^0\) virtual element discretization for a sixth-order elliptic equation ⋮ VEM and the mesh ⋮ The conforming virtual element method for polyharmonic and elastodynamics problems: a review ⋮ The virtual element method for the coupled system of magneto-hydrodynamics ⋮ Recent results and perspectives for virtual element methods

Uses Software

• Matlab

Cites Work

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