中文摘要：

超奇异积分的数值计算是边界元方法，尤其是在自然边界元方法中的重要的课题之一。基于矩形公式近似计算超奇异积分，得到相应的误差估计。在显示误差泛函的基础上，当误差展开式中的特殊函数等于零时，得到左（右）矩形公式的超收敛现象，此时，超收敛的收敛阶与经典的黎曼积分误差估计相同。相应的数值算例验证了理论分析的正确性。

英文摘要：

The numerical approximation of hypersingular integral is an important topic in boundary element methods especially in natural boundary element methods. Error estimate by rectangle rule to approximate hypersingular integral is obtained. Based on error functional, when the special function in the error functional equal zero, the super-convergence phenomenon of the left （right） rectangle rule is obtained, and convergent order is the same with one of classical Riemann integral. At last, several examples are presented to illustrate theoretical analysis.