BIT Numerical Mathematics

, Volume 56, Issue 2, pp 681–704 | Cite as

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

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Abstract

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.

Keywords

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

Mathematics Subject Classification

65M06 65M12 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Computational MathematicsLinköping UniversityLinköpingSweden

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