The actual error in the numerical solution of a boundary integral equation cannot be measured unless the true solution is known. Here it is shown that residual error in the H1/2 norm measures the actual error. Since the solution of the integral equation from the exterior Dirichlet problem for the two-dimensional Helmholtz equation with an arc as its boundary is unbounded near the tips, singular elements are used. The numerical results show that the use of the singular elements significantly reduces the error.
