Accuracy limit due to discretization in the boundary element method

The boundary element method (BEM) is one of the numerical methods for solving the boundary value problems under the integral scheme equivalent to the partial differential representation. In this paper we investigate the fundamental nature of the discretization errors inherent to the BEM. Numerical experiments conducted using new configuration models reveal: 1. The usual stepwise solution represents a very good approximation of the true solution sampled at regular intervals rather than the average value over each element. 2. The discretization errors thus evaluated against the sampled values show similar characteristics to those of the piecewise polynomial approximation in the numerical quadratures.