A Quasi-Conforming Point Interpolation Method (QC-PIM) for Elasticity Problems

作者：Xu, X.^*; Zheng, Z. Q.; Gu, Y. T.; Liu, G. R.

来源：International Journal of Computational Methods, 2016, 13(5): 1650026.

DOI：10.1142/S0219876216500262

• Point interpolation method
• quasi-conforming
• Galerkin formations
• patch test
• convergence

It is well known that a high-order point interpolation method (PIM) based on the standard Galerkin formations is not conforming, and thus the solution may not always be convergent. This paper proposes a new interesting technique called quasi-conforming point interpolation method (QC-PIM) for solving elasticity problems, by devising a novel scheme that smears the discontinuity. In the QC-PIM, the problem domain is first discretized by a set of background cells (typically triangles that can be automatically generated), and the average displacements on the interfaces of the two neighboring cells are assumed to be equal. We prove that when the size of background cells approaches to zero, all the additional potential energy coming from the discontinuous displacement field becomes zero, which ensures the pass of the standard patch test and hence the convergence. Numerical experiments verify that QC-PIM can produce the convergent solutions with higher accuracy and convergent rate that is in between fully conforming linear and quadratic models.

• 出版日期2016-10
• 单位吉林大学