Abstract
By potential theory, elastic problems with linear boundary conditions are converted into boundary integral equations (BIEs) with logarithmic and Cauchy singularity. In this paper, a mechanical quadrature method (MQMs) is presented to deal with the logarithmic and the Cauchy singularity simultaneously for solving the boundary integral equations. The convergence and stability are proved based on Anselone’s collective compact and asymptotical compact theory. Furthermore, an asymptotic expansion with odd powers of errors is presented, which possesses high accuracy order O(h3). Using h3−Richardson extrapolation algorithms (EAs), the accuracy order of the approximation can be greatly improved to O(h5), and an a posteriori error estimate can be obtained for constructing a self-adaptive algorithm. The efficiency of the algorithm is illustrated by examples.
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