Reproducing kernel element method. Part IV: Globally compatible Cn(n≥1) triangular hierarchy

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


In this part of the work, a globally compatible Cn(Ω) triangular element hierarchy is constructed in the framework of reproducing kernel element method (RKEM) for arbitrary two dimensional domains. In principle, the smoothness of the globally conforming element can be made arbitrarily high (n≥1). The triangle interpolation field can interpolate the derivatives of an unknown function up to arbitrary mth order, (Im), and it can reproduce complete kth order polynomials with k≥m. This is the first interpolation hierarchical structure that has ever been constructed with both minimal degrees of freedom and higher order smoothness and continuity over discretizations of a multiple dimensional domain. The performance of the newly constructed compatible element is evaluated in solving several Kirchhoff plate problems.

Original languageEnglish (US)
Pages (from-to)1013-1034
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Issue number12-14
StatePublished - Mar 26 2004


  • Finite element methods
  • Kirchhof plates
  • Meshfree methods
  • Triangle elements

ASJC Scopus subject areas

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

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