Splitting Extrapolations for Solving Boundary Integral Equations of Linear Elasticity Dirichlet Problems on Polygons by Mechanical Quadrature Methods

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.