Reproducing kernel element method. Part I: Theoretical formulation

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Least squares moving particle semi-implicit method (2014, methodology): “The first class of meshfree/ particle methods is used with various weak formulations such as Galerkin methods, for example, diffuse element method (DEM) [73], element free Gelerkin (EFG) method [11,13– 15,67], reproducing Kernel particle method (RKPM) [21, 63–65], h-p cloud method [27,28,58,74], par”
A moving Kriging interpolation‐based meshless method for numerical simulation of Kirchhoff plate problems (2009, methodology): “[21] have also investigated such plate problems by a minimal degree of freedom, arbitrary smooth, global compatible, Im/Cn interpolation hierarchy, both are built based on the framework of the reproducing kernel element method [22, 23].”
Reproducing Kernel Triangular B-spline-based FEM for Solving PDEs (2013, methodology): “Some examples include the moving least-square reproducing kernel method [22, 21], the reproducing kernel element method (RKEM) [29, 23, 34, 51] and the NURBS-based error reproducing kernel meshfree method (ERKM) [50].”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “A reproducing kernel element method (RKEM) that uses ﬁ nite element shape functions as the PU function with enriched bases has been proposed to achieve combined advantages of FEM (Kronecker-delta property) and polynomial reproducibility (Liu et al. 2004).”