Proof of Convergence for the Coupled Finite/Infinite Element Methods for Helmholtz Exterior Boundary-Value Problems

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: The sesquilinear form corresponding to the variational formulation is not positive-definite 1, 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. KeywordsHelmholtz EquationExterior DomainWeighted Sobolev SpaceInfinite ElementApproximate EigenvalueThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.