Well-posedness, stability and conservation for a discontinuous interface problem

Cristina La Cognata, Jan Nordström

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


The advection equation is studied in a completely general two domain setting with different wave-speeds and a time-independent jump-condition at the interface separating the domains. Well-posedness and conservation criteria are derived for the initial-boundary-value problem. The equations are semi-discretized using a finite difference method on Summation-By-Part (SBP) form. The relation between the stability and conservation properties of the approximation are studied when the boundary and interface conditions are weakly imposed by the Simultaneous-Approximation-Term (SAT) procedure. Numerical simulations corroborate the theoretical findings.

Original languageEnglish
Pages (from-to)681-704
Number of pages24
JournalBIT Numerical Mathematics
Issue number2
Publication statusPublished - 1 Jun 2016
Externally publishedYes


  • Conservation
  • Discontinuous coefficients problems
  • High order accuracy
  • Initial boundary value problems
  • Interface
  • Interface conditions
  • Stability
  • Summation-by-parts operators
  • Well-posedness

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics


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