Natural neighbour Galerkin methods

By Natarajan Sukumar, Brian Moran, Andrei Yu. Semenov, V. Belikov. 2001

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Polygonal finite elements for topology optimization: A unifying paradigm (2010, background): “Moreover, Laplace functions are linear on the boundary of the convex hull of {qi |i ∈I} [28], and satisfy the Kronecker-delta property: i (x j )= ij (9) This means that the interpolated value at a node is equal to the nodal value.”
Exact imposition of essential boundary condition and material interface continuity in Galerkin‐based meshless methods (2017, methodology): “If NEM [4] or NNGM [5] is used to analyze a material interface problem, some nodes should be deployed on the interface to assure the continuity.”
A Lagrangian meshless finite element method applied to fluid-structure interaction problems (2003, methodology): “Non-Sibsonian interpolations have the following properties [19].”
Polytope finite elements (2008, background): “It can be shown that the NECs are calculated based on the vertices of the facet [17, 18].”
Conforming polygonal finite elements (2004, background): “In a prior study [ 25 ], the Laplace interpolant was shown to reduce to finite element interpolation for certain specific cases: in 1D, the interpolant is identical to linear finite element interpolation and in 2D, if a point p has three neighbours, barycentric co-ordinates are obtained and for the ”
The meshless finite element method (2003, methodology): “Non-Sibsonian interpolations have several properties, which can be found in reference [ 16 ,18].”