Reproducing kernel element method. Part II: Globally conforming Im/Cn hierarchies

Shaofan Li*, Hongsheng Lu, Weimin Han, Wing Kam Liu, Daniel C. Simkins

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


In this part of the work, a minimal degrees of freedom, arbitrary smooth, globally compatible, Im/Cn interpolation hierarchy is constructed in the framework of reproducing kernel element method (RKEM) for arbitrary multiple dimensional domains. 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. The proposed hierarchical structure possesses the generalized Kronecker property, i.e.∂αΨ(β) I/∂xα(xJ)=δ IJδαβ, α,β≤m. This contribution is the latest breakthrough of an outstanding problem-construction of a minimal degrees of freedom, globally conforming, Im/Cn finite element interpolation fields on an arbitrary mesh or subdivision of multiple dimension. The newly constructed globally conforming interpolant is a hybrid of a set of C global partition polynomials with a highly 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)
Pages (from-to)953-987
Number of pages35
JournalComputer Methods in Applied Mechanics and Engineering
Issue number12-14
StatePublished - Mar 26 2004


  • Approximation theory
  • Finite element method
  • Meshfree method
  • Reproducing kernel element method

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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