Some virtual element methods for infinitesimal elasticity problems

DOI10.1007/978-3-030-95319-5_4zbMath1503.65285OpenAlexW4312701613MaRDI QIDQ2106422

Michele Visinoni, L. Patruno, Edoardo Artioli, Carlo Lovadina, Stefano de Miranda

Publication date: 14 December 2022

Full work available at URL: https://doi.org/10.1007/978-3-030-95319-5_4

zbMATH Keywords

linear elasticityvirtual element method

Mathematics Subject Classification ID

Linear elasticity with initial stresses (74B10) Finite element methods applied to problems in solid mechanics (74S05) Variational methods applied to PDEs (35A15) 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) PDEs in connection with mechanics of deformable solids (35Q74)

Uses Software

• ABAQUS
• Voro++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Virtual element methods for plate bending problems
• Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons
• Product Gauss cubature over polygons based on Green's integration formula
• A new discretization methodology for diffusion problems on generalized polyhedral meshes
• Non-conforming harmonic virtual element method: \(h\)- and \(p\)-versions
• High-order virtual element method on polyhedral meshes
• On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes
• A posteriori error estimates for the virtual element method
• A virtual element method for contact
• Arbitrary order 2D virtual elements for polygonal meshes: I: Elastic problem
• Arbitrary order 2D virtual elements for polygonal meshes. II: Inelastic problem
• BDDC and FETI-DP for the virtual element method
• Efficient virtual element formulations for compressible and incompressible finite deformations
• Exploring high-order three dimensional virtual elements: bases and stabilizations
• Virtual element method for geomechanical simulations of reservoir models
• Mixed finite elements for elasticity
• A family of virtual element methods for plane elasticity problems based on the Hellinger-Reissner principle
• High-order virtual element method for the homogenization of long fiber nonlinear composites
• A simple and effective gradient recovery scheme and \textit{a posteriori} error estimator for the virtual element method (VEM)
• Bricks for the mixed high-order virtual element method: projectors and differential operators
• Virtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulation
• Curvilinear virtual elements for contact mechanics
• An enhanced VEM formulation for plane elasticity
• On nonconvex meshes for elastodynamics using virtual element methods with explicit time integration
• Curvilinear virtual elements for 2D solid mechanics applications
• A three-dimensional Hellinger-Reissner virtual element method for linear elasticity problems
• Algebraic cubature on polygonal elements with a circular edge
• Gauss-Green cubature and moment computation over arbitrary geometries
• Some estimates for virtual element methods
• Some basic formulations of the virtual element method (VEM) for finite deformations
• A stress/displacement virtual element method for plane elasticity problems
• Mixed virtual element methods for elastodynamics with weak symmetry
• A virtual element method for elastic and inelastic problems on polytope meshes
• The mimetic finite difference method for elliptic problems
• 3D mixed virtual element formulation for dynamic elasto-plastic analysis
• Virtual Elements for Linear Elasticity Problems
• Divergence free virtual elements for the stokes problem on polygonal meshes
• Compression of Multivariate Discrete Measures and Applications
• Mimetic finite differences for elliptic problems
• Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
• Virtual element methods on meshes with small edges or faces
• Stability analysis for the virtual element method
• A Family of Three-Dimensional Virtual Elements with Applications to Magnetostatics
• Centroidal Voronoi Tessellations: Applications and Algorithms
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• Mixed Finite Element Methods and Applications
• A residual a posteriori error estimate for the Virtual Element Method
• Hybridization of the virtual element method for linear elasticity problems
• The Hitchhiker's Guide to the Virtual Element Method
• The Virtual Element Method with curved edges
• Residuala posteriorierror estimation for the Virtual Element Method for elliptic problems
• Generalized Gaussian quadrature rules on arbitrary polygons
• A virtual element method with arbitrary regularity

This page was built for publication: Some virtual element methods for infinitesimal elasticity problems