Reproducing kernel element interpolation: Globally conforming Im/Cn/Pk Hierarchies

Shaofan Li*, Daniel C. Simkins, Hongsheng Lu, Wing K Liu

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations


In this work, arbitrarily smooth, globally compatible, Im/Cn/Pk interpolation hierarchies are constructed in the framework of reproducing kernel element method (RKEM) for multi-dimensional domains. This is the first interpolation hierarchical structure that has been ever constructed with both minimal degrees of freedom and higher order continuity and reproducing conditions over multi-dimensional domains. The proposed hierarchical structure possesses the generalized Kronecker property, i.e., ∂αΨI (β)/∂xα(xJ) = δIJδαβ, {pipe}α{pipe}, {pipe}β{pipe} ≤ m. The newly constructed globally conforming interpolant is a hybrid of global partition polynomials (C) and a smooth (Cn) compactly supported meshfree partition of unity. Examples of compatible RKEM hierarchical interpolations are illustrated, and they are used in a Galerkin procedure to solve differential equations.

Original languageEnglish (US)
Title of host publicationMeshfree Methods for Partial Differential Equations II
Number of pages24
StatePublished - Dec 1 2005

Publication series

NameLecture Notes in Computational Science and Engineering
ISSN (Print)1439-7358

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Engineering
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics


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