Is the one-equation coupling of finite and boundary elements always stable?

Günther Of, Olaf Steinbach*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper we present a sufficient and necessary condition to ensure the ellipticity of the bilinear form which is related to the one-equation coupling of finite and boundary element methods to solve a scalar free space transmission problem for a second order uniform elliptic partial differential equation in the case of general Lipschitz interfaces. This condition relates the minimal eigenvalue of the coefficient matrix in the bounded interior domain to the contraction constant of the shifted double layer integral operator which reflects the shape of the interface. This paper extends and improves earlier results [12] on sufficient conditions, but now includes also necessary conditions. Numerical examples confirm the theoretical results on the sharpeness of the presented estimates.
Original languageEnglish
Pages (from-to)476-484
JournalZeitschrift für Angewandte Mathematik und Mechanik
Issue number6-7
Publication statusPublished - 2013

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)
  • Theoretical

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