On hp- error estimation in the BEM for a three-dimensional Helmholtz exterior problem Original Research Article

The purpose of the paper is to give an a priori convergence estimate for the hp-adaptive boundary element method. The method is used to solve an exterior Helmholtz boundary-value problem with the Robinʹs boundary condition in the three-dimensional space. The mathematical model describes an acoustic wave scattering problem on a bounded elastic solid, where time-harmonic process is assumed. The estimate consists of three parts, which correspond to influence of three errors, caused by interpolation of functions, geometry and an incident wave.