Reproducing kernel triangular B-spline-based FEM for solving PDEs
- Authors
- Jia, Yue; Zhang, Yongjie; Xu, Gang; Zhuang, Xiaoying; Rabczuk, Timon
- Issue Date
- 1-12월-2013
- Publisher
- ELSEVIER SCIENCE SA
- Keywords
- Triangular B-spline; Reproducing kernel triangular B-spline; Finite element method; Reproducing kernel approximation; Poisson' s equations
- Citation
- COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, v.267, pp.342 - 358
- Indexed
- SCIE
SCOPUS
- Journal Title
- COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
- Volume
- 267
- Start Page
- 342
- End Page
- 358
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/101330
- DOI
- 10.1016/j.cma.2013.08.019
- ISSN
- 0045-7825
- 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. (C) 2013 Elsevier B.V. All rights reserved.
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