Weak solvability of interior transmission problems via mixed finite elements and Dirichlet to Neumann mappings

Gabriel R. Barrenechea, Gabriel N. Gatica, George C. Hsiao

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6 Citations (Scopus)


We study the weak solvability of an interior linear-nonlinear transmission problem arising in steady heat transfer and potential theory. For the variational formulation, we use a Dirichlet-to-Neumann mapping on the interface, which is obtained from the application of the boundary integral method to the linear domain, and we utilize a mixed finite element method in the nonlinear region. Existence and uniqueness of solution for the continuous formulation are provided and general approximation results for a fully discrete Galerkin method are derived. In particular, a compatibility condition between the mesh sizes involved is deduced in order to conclude the solvability and stability of this Galerkin scheme.
Original languageEnglish
Pages (from-to)145-160
Number of pages16
JournalJournal of Computational and Applied Mathematics
Issue number2
Publication statusPublished - 3 Mar 1999



  • transmission problems
  • Dirichlet-to-Neumann mapping
  • boundary integral method
  • mixed finite element
  • non-conforming Galerkin scheme

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