Reproducing kernel triangular B-spline-based FEM for solving PDEs

Yue Jia, Yongjie Zhang, Gang Xu, Xiaoying Zhuang, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)


We propose a reproducing kernel triangular B-spline-based finite element method (FEM) as an improvement to the conventional triangular B-spline element for solving partial differential equations (PDEs). In the latter, unexpected errors can occur throughout the analysis domain mainly due to the excessive flexibilities in defining the B-spline. The performance therefore becomes unstable and cannot be controlled in a desirable way. To address this issue, the proposed improvement adopts the reproducing kernel approximation in the calculation of B-spline kernel function. Three types of PDE problems are tested to validate the present element and compare against the conventional triangular B-spline. It has been shown that the improved triangular B-spline satisfies the partition of unity condition even for extreme conditions including corners and holes.

Original languageEnglish
Pages (from-to)342-358
Number of pages17
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2013 Dec 1

Bibliographical note

Funding Information:
The authors thank the support by the European Union through the FP7-grant ITN (Marie Curie Initial Training Networks) INSIST (Integrating Numerical Simulation and Geometric Design Technology), the US Office of Navy Research through the ONR-YIP award N00014–10-1–0698, the NSFC (41130751), National Basic Research Program of China (973 Program: 2011CB013800) and Shanghai Pujiang Program (12PJ1409100), the Nature Science Foundation of China (Nos. 61272390 , 61004117 , 61211130103 ) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars from State Education Ministry.


  • Finite element method
  • Poisson's equations
  • Reproducing kernel approximation
  • Reproducing kernel triangular B-spline
  • Triangular B-spline

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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