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

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

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

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
Volume267
DOIs
Publication statusPublished - 2013 Dec 1

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splines
Splines
partial differential equations
Partial differential equations
finite element method
Finite element method
spline functions
kernel functions
unity
partitions
flexibility
approximation

Keywords

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

ASJC Scopus subject areas

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

Cite this

Reproducing kernel triangular B-spline-based FEM for solving PDEs. / Jia, Yue; Zhang, Yongjie; Xu, Gang; Zhuang, Xiaoying; Rabczuk, Timon.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 267, 01.12.2013, p. 342-358.

Research output: Contribution to journalArticle

Jia, Yue ; Zhang, Yongjie ; Xu, Gang ; Zhuang, Xiaoying ; Rabczuk, Timon. / Reproducing kernel triangular B-spline-based FEM for solving PDEs. In: Computer Methods in Applied Mechanics and Engineering. 2013 ; Vol. 267. pp. 342-358.
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