The Least-Squares Meshfree Finite Element Method

Bonan Jiang () and Guojun Liao
Additional contact information
Bonan Jiang: Oakland University, Department of Mathematics and Statistics
Guojun Liao: The University of Texas at Arlington, Department of Mathematics

A chapter in Computational Mechanics, 2007, pp 341-341 from Springer

Abstract: Abstract Most meshfree methods are based on the Galerkin principle and employ the moving least-squares approximation for construction of shape functions [1]. Although there is no need for an explicit mesh in the construction of moving least-squares shape functions, a separate background mesh is required to integrate the weak form, so they are not truly meshfree methods. Due to the non-interpolative character of the moving least-squares approximation, the enforcement of essential boundary conditions in the Galerkin formulation is quite awkward. Moreover, the moving least-squares approximation is more expensive computationally than the finite element interpolation. In this research, we have developed a least-squares meshfree particle finite element method which combines the features of the least-squares finite element method [2] and the meshfree particle method [3]. The least-squares finite element method which is based on minimization of the L2 norm of the residuals of a first-order system of differential equations, is a simple, efficient and robust technique, and can solve almost any kind of partial differential equation with the same mathematical/computational formulation. Since the least-squares method doesn’t make use of the integration by parts for converting domain integration into boundary integration, and the meshfree particle method employs the usual finite element interpolations based on particles, all troubles that plague the Garlerkin-based meshfree methods disappear. Numerical examples show that the proposed method possesses superconvergence for elasticity and thin plate bending problems.

Keywords: Finite Element Method; Boundary Integration; Meshless Method; Meshfree Method; Robust Technique (search for similar items in EconPapers)
Date: 2007
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-75999-7_141

Ordering information: This item can be ordered from
http://www.springer.com/9783540759997

DOI: 10.1007/978-3-540-75999-7_141

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().