Provably non-stiff implementation of weak coupling conditions for hyperbolic problems

Ossian O’Reilly, Jan Nordström

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In the context of coupling hyperbolic problems, the maximum stable time step of an explicit numerical scheme may depend on the design of the coupling procedure. If this is the case, the coupling procedure is sensitive to changes in model parameters independent of the Courant–Friedrichs–Levy condition. This sensitivity can cause artificial stiffness that degrades the performance of a numerical scheme. To overcome this problem, we present a systematic and general procedure for weakly imposing coupling conditions via penalty terms in a provably non-stiff manner. The procedure can be used to construct both energy conservative and dissipative couplings, and the user is given control over the amount of dissipation desired. The resulting formulation is simple to implement and dual consistent. The penalty coefficients take the form of projection matrices based on the coupling conditions. Numerical experiments demonstrate that this procedure results in both optimal spectral radii and superconvergent linear functionals.

Original languageEnglish
Pages (from-to)551-589
Number of pages39
JournalNumerische Mathematik
Issue number2
Publication statusPublished - Feb 2022

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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