BEM and estimate of actual error for exterior Dirichlet problem for two- dimensional Helmholtz equation (Q1803720)

In the general situation the actual error in the numerical solution of a boundary integral equation cannot be measured unless the true solution is known. The author shows that the residual error in the \(H^{1/2}\) norm measures the acutal error for a test problem which is an exterior Dirichlet problem for the two-dimensional Helmholtz equation with an arc as its boundary. Since the solutions is unbounded near the tips, singular elements are used. The numerical results show that the use of the singular elements significantly reduces the error.