Volume 24, Issue 1
Splitting Extrapolations for Solving Boundary Integral Equations of Linear Elasticity Dirichlet Problems on Polygons by Mechanical Quadrature Methods
DOI:

J. Comp. Math., 24 (2006), pp. 9-18

Published online: 2006-02

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• Abstract

Taking $h_m$ as the mesh width of a curved edge $\Gamma _m$ $(m=1,...,d$ ) of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first kind of plane elasticity Dirichlet problems on curved polygons, which possess high accuracy $O(h_0^3)$ and low computing complexities. Since multivariate asymptotic expansions of approximate errors with power $h_i^3$ $(i=1,2,...,d)$ are shown, by means of the splitting extrapolations high precision approximations and a posteriori estimate are obtained.

• Keywords

Splitting extrapolation Linear elasticity Dirichlet problem Boundary integral equation of the first kind Mechanical quadrature method

@Article{JCM-24-9, author = {}, title = {Splitting Extrapolations for Solving Boundary Integral Equations of Linear Elasticity Dirichlet Problems on Polygons by Mechanical Quadrature Methods}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {1}, pages = {9--18}, abstract = { Taking $h_m$ as the mesh width of a curved edge $\Gamma _m$ $(m=1,...,d$ ) of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first kind of plane elasticity Dirichlet problems on curved polygons, which possess high accuracy $O(h_0^3)$ and low computing complexities. Since multivariate asymptotic expansions of approximate errors with power $h_i^3$ $(i=1,2,...,d)$ are shown, by means of the splitting extrapolations high precision approximations and a posteriori estimate are obtained. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8729.html} }
TY - JOUR T1 - Splitting Extrapolations for Solving Boundary Integral Equations of Linear Elasticity Dirichlet Problems on Polygons by Mechanical Quadrature Methods JO - Journal of Computational Mathematics VL - 1 SP - 9 EP - 18 PY - 2006 DA - 2006/02 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8729.html KW - Splitting extrapolation KW - Linear elasticity Dirichlet problem KW - Boundary integral equation of the first kind KW - Mechanical quadrature method AB - Taking $h_m$ as the mesh width of a curved edge $\Gamma _m$ $(m=1,...,d$ ) of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first kind of plane elasticity Dirichlet problems on curved polygons, which possess high accuracy $O(h_0^3)$ and low computing complexities. Since multivariate asymptotic expansions of approximate errors with power $h_i^3$ $(i=1,2,...,d)$ are shown, by means of the splitting extrapolations high precision approximations and a posteriori estimate are obtained.