Coupling requirements for multiphysics problems posed on two domains

Fatemeh Ghasemi, Jan Nordström

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We consider two hyperbolic systems in first order form of different size posed on two domains. Our ambition is to derive general conditions for when the two systems can and cannot be coupled. The adjoint equations are derived and well-posedness of the primal and dual problems is discussed. By applying the energy method, interface conditions for the primal and dual problems are derived such that the continuous problems are well posed. The equations are discretized using a high order finite difference method in summation-by-parts form and the interface conditions are imposed weakly in a stable way, using penalty formulations. It is shown that one specific choice of penalty matrices leads to a dual consistent scheme. By considering an example, it is shown that the correct physical coupling conditions are contained in the set of well posed coupling conditions. It is also shown that dual consistency leads to superconverging functionals and reduced stifiness.

Original languageEnglish
Pages (from-to)2885-2904
Number of pages20
JournalSIAM Journal on Numerical Analysis
Issue number6
Publication statusPublished - 2017
Externally publishedYes


  • Dual consistency
  • High order finite differences
  • Stability
  • Stifiness
  • Summation-by-parts
  • Superconvergence
  • Weak interface conditions
  • Well posed problems

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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