Error estimates of the finite element method for the exterior Helmholtz problem with a modified DtN boundary condition

A priori error estimates in the H 1 - and L 2 -norms are established for the finite element method applied to the exterior Helmholtz problem, with modified Dirichlet-to-Neumann (MDtN) boundary condition. The error estimates include the effect of truncation of the MDtN boundary condition as well as that of discretization of the finite element method. The error estimate in the L 2 -norm is sharper than that obtained by the author [D. Koyama, Error estimates of the DtN finite element method for the exterior Helmholtz problem, J. Comput. Appl. Math. 200 (1) (2007) 21–31] for the truncated DtN boundary condition.