Abstract
The note outlines the idea of coupled Finite Element (FE) — Infinite Element (IE) approximations for the exterior Helmholtz equation and summarizes the convergence analysis presented in [6]. The main difficulty in analyzing the convergence of approximations to the Helmholtz equation in exterior domains lies in two facts:
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The sesquilinear form corresponding to the variational formulation is not positive-definite 1,
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The weighted Sobolev space for exterior domains is riot compactly imbedded in the L 2-space and therefore the standard asymptotic convergence argument [4] cannot be applied.
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Demkowicz, L., Ihlenburg, F. (1998). Proof of Convergence for the Coupled Finite/Infinite Element Methods for Helmholtz Exterior Boundary-Value Problems. In: Geers, T.L. (eds) IUTAM Symposium on Computational Methods for Unbounded Domains. Fluid Mechanics and Its Applications, vol 49. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9095-2_9
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DOI: https://doi.org/10.1007/978-94-015-9095-2_9
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