Recent developments in stabilized Galerkin and collocation meshfree methods

  • Chen Jiun-Shyan Department of Civil & Environmental Engineering, University of California
  • Chi Sheng-Wei Department of Civil & Environmental Engineering, University of California
  • Hu Hsin-Yun Department of Mathematics Tunghai University

Abstract

Meshfree methods have been developed based on Galerkin type weak formulation and strong formulation with collocation. Galerkin type formulation in conjunction with the compactly supported approximation functions and polynomial reproducibility yields algebraic convergence, while strong form collocation method with nonlocal approximation such as radial basis functions offers exponential convergence. In this work, we discuss rank instability resulting from the nodal integration of Galerkin type meshfree method as well as the ill-conditioning type instability in the radial basis collocation method. We present the recent advances in resolving these difficulties in meshfree methods, and demonstrate how meshfree methods can be applied to problems difficult to be modeled by the conventional finite element methods due to their intrinsic regularity constraints.

Keywords

meshfree methods, stabilization method, collocation method, reproducing kernel,

References

Published
Jan 25, 2017
How to Cite
JIUN-SHYAN, Chen; SHENG-WEI, Chi; HSIN-YUN, Hu. Recent developments in stabilized Galerkin and collocation meshfree methods. Computer Assisted Methods in Engineering and Science, [S.l.], v. 18, n. 1–2, p. 3–21, jan. 2017. ISSN 2299-3649. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/117>. Date accessed: 10 dec. 2022.
Section
Articles