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.
Citation
Jin Huang. Zi Cai Li. Tao L¨u. Rui Zhu. "SPLITTING EXTRAPOLATIONS FOR SOLVING BOUNDARY INTEGRAL EQUATIONS OF MIXED BOUNDARY CONDITIONS ON POLYGONS BY MECHANICAL QUADRATURE METHODS." Taiwanese J. Math. 12 (9) 2341 - 2361, 2008. https://doi.org/10.11650/twjm/1500405183
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