Skip to main content

Error Analysis of the DtN-FEM for the Scattering Problem in Acoustics via Fourier Analysis

Resource type
Date created
2011
Authors/Contributors
Author: Xu, Liwei
Abstract
In this paper, we are concerned with the error analysis for the nite elementsolution of the two-dimensional exterior Neumann boundary value problem inacoustics. In particular, we establish an explicit priori error estimates in H1and L2- norms including both the e ect of the truncation of the DtN mappingand that of the numerical discretization. To apply the nite element method(FEM) to the exterior problem, the original boundary value problem is reducedto an equivalent nonlocal boundary value problem via a Dirichlet-to-Neumann(DtN) mapping represented in terms of the Fourier expansion series. We discussessential features of the corresponding variational equation and its modi cationdue to the truncation of the DtN mapping in appropriate function spaces. Nu-merical tests are presented to validate our theoretical results.
Document
Copyright statement
Copyright is held by the author(s).
Permissions
You are free to copy, distribute and transmit this work under the following conditions: You must give attribution to the work (but not in any way that suggests that the author endorses you or your use of the work); You may not use this work for commercial purposes.
Scholarly level
Peer reviewed?
Yes
Language
English
Member of collection

Views & downloads - as of June 2023

Views: 0
Downloads: 0