Hongsheng Lu

TL;DR: This paper introduces and analyzes a new class of methods, collectively called the reproducing kernel element method (RKEM), to combine the strengths of both finite element methods (FEM) and meshfree methods, and presents a rigorous error analysis and convergence study of the method.

TL;DR: In this article, the Reproducing Kernel Element Method (RKEM) was used to simulate the microextrusion problem, and the effect of grain size was investigated by using workpieces heat treated to produce grain sizes varying from 32 μm up to 211 μm.

TL;DR: This is the first interpolation hierarchical structure that has been constructed with both minimal degrees of freedom and higher order smoothness or continuity over multi-dimensional domain, and possesses the generalized Kronecker property.

TL;DR: Without refining mesh, high order consistency in interpolation hierarchy with generalized Kronecker delta property can be straightforwardly achieved in quadrilateral and triangular mesh in 2D by the proposed scheme.

TL;DR: In this article, a globally compatible C n ðXÞ triangular element hierarchy is constructed in the framework of reproducing kernel element method (RKEM) for arbitrary two dimensional domains.