Abstract
The computation of trapezoidal rule for the supersingular integrals on a circle in boundary element methods is discussed. When the singular point coincides with some priori known point, the convergence rate of the trapezoidal rule is higher than the global one which is considered as the superconvergence phenomenon. Then the error functional of density function is derived and the superconvergence phenomenon of composite trapezoidal rule occurs at certain local coordinate of each subinterval. At last, several numerical examples are provided to validate the theoretical analysis and show the efficiency of the algorithms.
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