Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods
Abstract
It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can be used to solve the Helmholtz equation in unbounded domains. In this work, applying such DtN boundary condition and using the finite element method, we analyze and solve a two dimensional transmission problem describing elastic waves inside a bounded and closed elastic obstacle and acoustic waves outside it. We are mainly interested in analyzing the DtN boundary condition of the Helmholtz equation in order to establish the well-posedness results of the approximated variational equation, and further derive a priori error estimates involving effects of both the finite element discretization and the truncation of DtN map. Finally, some numerical results are presented to illustrate the accuracy of the numerical scheme.
Additional Information
© 2021 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature. Received 07 August 2018; Revised 20 January 2021; Accepted 09 March 2021; Published 25 March 2021. The work of L. Xu is partially supported by a Key Project of the Major Research Plan of NSFC (No. 91630205), and NSFC Grant (11771068, 12071060), and he also would like to thank Prof. G.C. Hsiao and Prof. J.E. Pasciak for their invaluable encouragements and suggestions which are of great importance for the completion of this work.Attached Files
Submitted - 1609.00583.pdf
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Additional details
- Alternative title
- A priori error estimates of the DtN-FEM: fluid-solid interaction problems
- Eprint ID
- 108564
- DOI
- 10.1007/s00211-021-01195-7
- Resolver ID
- CaltechAUTHORS:20210325-155505378
- 91630205
- National Natural Science Foundation of China
- 11771068
- National Natural Science Foundation of China
- 12071060
- National Natural Science Foundation of China
- Created
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2021-03-25Created from EPrint's datestamp field
- Updated
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2021-04-22Created from EPrint's last_modified field