Error Analysis of the DtN Finite Element Method for the Linear Water Wave Scattering Problem due to Stationary Bodies(Theory,<Special Topics>Activity Group "Scientific Computation and Numerical Analysis")

Abstract

An a priori error estimate of the DtN (Drichlet-to-Neumann) finite element method for the linear water wave scattering problem due to bodies without forward speed in a 3D infinite water region with finite depth is established. The estimate accounts for the effects of truncation of infinite Fourier series representing the DtN boundary condition as well as of discretization of the finite element method. To estimate the error due to the truncation, several properties of the Hankel functions and the modihed Bessel functions are demonstrated.