Consistent and stable meshfree Galerkin methods using the virtual element decomposition

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)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Effect of numerical integration on meshless methods
Maximum-entropy meshfree method for compressible and near-incompressible elasticity
Integration constraint in diffuse element method
Meshless methods: a review and computer implementation aspects
Generalizing the finite element method: Diffuse approximation and diffuse elements
Meshless methods: An overview and recent developments
Nodal integration of the element-free Galerkin method
Consistent pseudo-derivatives in meshless methods
A four-point integration scheme with quadratic exactness for three-dimensional element-free Galerkin method based on variationally consistent formulation
On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes
Volume-averaged nodal projection method for nearly-incompressible elasticity using meshfree and bubble basis functions
Improved robustness for nearly-incompressible large deformation meshfree simulations on Delaunay tessellations
Virtual Elements for Linear Elasticity Problems
Second-order accurate derivatives and integration schemes for meshfree methods
An arbitrary order variationally consistent integration for Galerkin meshfree methods
Consistent element-free Galerkin method
Hourglass stabilization and the virtual element method
Gradient correction for polygonal and polyhedral finite elements
Localmaximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods
Overview and construction of meshfree basis functions: from moving least squares to entropy approximants
Quadrature for meshless methods
Meshfree and finite element nodal integration methods
Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods
BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
The Hitchhiker's Guide to the Virtual Element Method
New perspectives on polygonal and polyhedral finite element methods
Addressing integration error for polygonal finite elements through polynomial projections: A patch test connection
A virtual element method with arbitrary regularity
Construction of polygonal interpolants: a maximum entropy approach