TY - JOUR
T1 - Galerkin Boundary Node Method for Exterior Neumann Problems
AU - Xiaolin Li & Jialin Zhu
JO - Journal of Computational Mathematics
VL - 3
SP - 243
EP - 260
PY - 2011
DA - 2011/06
SN - 29
DO - http://doi.org/10.4208/jcm.1010-m3069
UR - https://global-sci.org/intro/article_detail/jcm/8477.html
KW - Meshless, Galerkin boundary node method, Boundary integral equations, Moving least-squares, Error estimate
AB - <p style="text-align: justify;">In this paper, we present a meshless Galerkin scheme of boundary integral equations (BIEs), known as the Galerkin boundary node method (GBNM), for two-dimensional exterior Neumann problems that combines the moving least-squares (MLS) approximations and a variational formulation of BIEs. In this approach, boundary conditions can be implemented directly despite the MLS approximations lack the delta function property. Besides, the GBNM keeps the symmetry and positive definiteness of the variational problems. A rigorous error analysis and convergence study of the method is presented in Sobolev spaces. Numerical examples are also given to illustrate the capability of the method.</p>