Taiwanese Journal of Mathematics

SPLITTING EXTRAPOLATIONS FOR SOLVING BOUNDARY INTEGRAL EQUATIONS OF MIXED BOUNDARY CONDITIONS ON POLYGONS BY MECHANICAL QUADRATURE METHODS

Jin Huang, Zi Cai Li, Tao L¨u, and Rui Zhu

Full-text: Open access

Abstract

To solve the boundary integral equations (BIE) of mixed boundary conditions, we propose the mechanical quadrature methods (MQM) using specific quadrature rule to deal with weakly singular integrals. Denote $h_{m}$ as the mesh width of a curved edge $\Gamma_{m}$ ($m=1,...,d)$ of polygons. Then the multivariate asymptotic expansions of solution errors are found to be $O(h^{3}),$ where $h=\max_{1\leq m\leq d}h_{m}.$ Hence, by using the splitting extrapolation methods (SEM), the high convergence rates as $O(h^{5})$ can be achieved. Moreover, numerical examples are provided to support our theoretical analysis.

Article information

Source
Taiwanese J. Math., Volume 12, Number 9 (2008), 2341-2361.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405183

Digital Object Identifier
doi:10.11650/twjm/1500405183

Mathematical Reviews number (MathSciNet)
MR2479059

Zentralblatt MATH identifier
1176.65142

Subjects
Primary: 65R20: Integral equations 45L10

Keywords
mixed boundary condition polygon mechanical quadrature method splitting extrapolation boundary integral equation

Citation

Huang, Jin; Li, Zi Cai; L¨u, Tao; Zhu, Rui. SPLITTING EXTRAPOLATIONS FOR SOLVING BOUNDARY INTEGRAL EQUATIONS OF MIXED BOUNDARY CONDITIONS ON POLYGONS BY MECHANICAL QUADRATURE METHODS. Taiwanese J. Math. 12 (2008), no. 9, 2341--2361. doi:10.11650/twjm/1500405183. https://projecteuclid.org/euclid.twjm/1500405183


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