Error estimates of the DtN finite element method for the exterior Helmholtz problem

Authors:
Daisuke Koyama
Affiliations:
Department of Computer Science, The University of Electro-Communications, Chofugaoka 1-5-1, Chofu, Tokyo 182-8585, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

A priori error estimates are established for the DtN (Dirichlet-to-Neumann) finite element method applied to the exterior Helmholtz problem. The error estimates include the effect of truncation of the DtN boundary condition as well as that of the finite element discretization. A property of the Hankel functions which plays an important role in the proof of the error estimates is introduced.