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

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Dirichlet-to-Neumann mapping
Error analysis
Finite element method
Acoustic scattering problem

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.

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Hsiao, G. C., Nigam, N., Pasciak, J. E., & Xu, L. (2011). Error analysis of the DtN-FEM for the scattering problem in acoustics via fourier analysis. Journal of Computational and Applied Mathematics, 235(17), 4949-4965. doi:10.1016/