TY - JOUR
T1 - Optimal Error Estimates of the Partition of Unity Method with Local Polynomial Approximation Spaces
JO - Journal of Computational Mathematics
VL - 3
SP - 365
EP - 372
PY - 2006
DA - 2006/06
SN - 24
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8758.html
KW - Meshless methods, Partition of unity finite element method(PUFEM), Error
estimate.
AB - <p style="text-align: justify;">In this paper, we provide a theoretical analysis of the partition of unity finite element method(PUFEM), which belongs to the family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations [12]. Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in 1-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems.</p>