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 - 2013/9/11

Y1 - 2013/9/11

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

VL - 267

SP - 342

EP - 358

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -