TY - JOUR
T1 - Reproducing kernel triangular B-spline-based FEM for solving PDEs
AU - Jia, Yue
AU - Zhang, Yongjie
AU - Xu, Gang
AU - Zhuang, Xiaoying
AU - Rabczuk, Timon
N1 - 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.
PY - 2013/12/1
Y1 - 2013/12/1
N2 - 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.
AB - 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.
KW - Finite element method
KW - Poisson's equations
KW - Reproducing kernel approximation
KW - Reproducing kernel triangular B-spline
KW - Triangular B-spline
UR - http://www.scopus.com/inward/record.url?scp=84884964050&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2013.08.019
DO - 10.1016/j.cma.2013.08.019
M3 - Article
AN - SCOPUS:84884964050
SN - 0045-7825
VL - 267
SP - 342
EP - 358
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -