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Error bounds of singular boundary method for potential problems
Author(s) -
Li Junpu,
Chen Wen,
Gu Yan
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22176
Subject(s) - mathematics , discretization , boundary (topology) , singular boundary method , collocation (remote sensing) , boundary element method , convergence (economics) , benchmark (surveying) , mathematical analysis , finite element method , computer science , physics , geodesy , machine learning , geography , economics , thermodynamics , economic growth
The singular boundary method (SBM) is a recent strong‐form boundary collocation method free of integration, mesh, and fictitious boundary. Although an extensive study has been reported in the literature on improving its accuracy and stability as well as its applications to diverse problems, little, however, has been done to analyze its convergence mathematically. The main purpose of this paper is to derive the explicit error bounds of the SBM for potential problems as well as to explain the essential difference between the origin intensity factor (OIF) in the SBM and the singular integration in the boundary element method (BEM). In the process of derivation, we also illustrate the physical meaning of OIF and explain the reason why the OIF has the function to correct the discretization error on the boundary. Finally, several benchmark examples are given to verify the effectiveness of the conclusions obtained from this article, as well as to investigate the different convergence behaviors between the SBM and BEM. It can be found that the SBM has the explicit error bound and is mathematically a stable technique.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1987–2004, 2017