On the coupling of boundary integral and finite element methods with nonlinear transmission conditions

Gabriel R. Barrenechea, Gabriel N. Gatica

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Abstract

We apply the coupling of boundary integral and finite element methods to study the weak solvability of certain exterior boundary value problems with nonlinear transmission conditions. As a model we consider a nonlinear second order elliptic equation in divergence form in a bounded inner region of the plane coupled with the Laplace equation in the corresponding exterior domain. The flux jump across the common nonlinear-linear interface is unknown and assumed to depend nonlinearly on the Dirichlet data. We establish the associated variational formulation in an operator equation setting and provide existence, uniqueness and approximation results.
Original languageEnglish
Pages (from-to)181-210
Number of pages30
JournalApplicable Analysis
Volume62
Issue number1-2
DOIs
Publication statusPublished - 1 May 1996

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Keywords

  • boundary integral method
  • finite elements
  • coupling procedure
  • nonlinear flux

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