TY - JOUR

T1 - On error control in the element-free Galerkin method

AU - Zhuang, Xiaoying

AU - Heaney, Claire

AU - Augarde, Charles

N1 - Funding information: The first author is supported by a Dorothy Hodgkin Postgraduate Award from the UK EPSRC . Part of the work described here was supported by Grant ref EP/D077117/01 and Kwang-Hua Fund for College of Civil Engineering, Tongji University.

PY - 2011/10/26

Y1 - 2011/10/26

N2 - The paper investigates discretisation error control in the element-free Galerkin method (EFGM) highlighting the differences from the finite element method (FEM). We demonstrate that the (now) conventional procedures for error analysis used in the finite element method require careful application in the EFGM, otherwise competing sources of error work against each other. Examples are provided of previous works in which adopting an FEM-based approach leads to dubious refinements. The discretisation error is here split into contributions arising from an inadequate number of degrees of freedom e h, and from an inadequate basis e p. Numerical studies given in this paper show that for the EFGM the error cannot be easily split into these component parts. Furthermore, we note that arbitrarily setting the size of nodal supports (as is commonly proposed in many papers) causes severe difficulties in terms of error control and solution accuracy. While no solutions to this problem are presented in this paper it is important to highlight these difficulties in applying an approach to errors from the FEM in the EFGM. While numerical tests are performed only for the EFGM, the conclusions are applicable to other meshless methods based on the concept of nodal support.

AB - The paper investigates discretisation error control in the element-free Galerkin method (EFGM) highlighting the differences from the finite element method (FEM). We demonstrate that the (now) conventional procedures for error analysis used in the finite element method require careful application in the EFGM, otherwise competing sources of error work against each other. Examples are provided of previous works in which adopting an FEM-based approach leads to dubious refinements. The discretisation error is here split into contributions arising from an inadequate number of degrees of freedom e h, and from an inadequate basis e p. Numerical studies given in this paper show that for the EFGM the error cannot be easily split into these component parts. Furthermore, we note that arbitrarily setting the size of nodal supports (as is commonly proposed in many papers) causes severe difficulties in terms of error control and solution accuracy. While no solutions to this problem are presented in this paper it is important to highlight these difficulties in applying an approach to errors from the FEM in the EFGM. While numerical tests are performed only for the EFGM, the conclusions are applicable to other meshless methods based on the concept of nodal support.

KW - Adaptivity

KW - EFG

KW - Error control

KW - Meshless

UR - http://www.scopus.com/inward/record.url?scp=80054848577&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2011.06.011

DO - 10.1016/j.enganabound.2011.06.011

M3 - Article

AN - SCOPUS:80054848577

VL - 36

SP - 351

EP - 360

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

SN - 0955-7997

IS - 3

ER -