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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.

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Authors and Affiliations

  1. Department of Mathematics, Computational Mathematics, Linköping University, 581 83, Linköping, Sweden

    Cristina La Cognata & Jan Nordström

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  1. Cristina La Cognata
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  2. Jan Nordström
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Correspondence to Cristina La Cognata.

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Communicated by Jan Hesthaven.

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La Cognata, C., Nordström, J. Well-posedness, stability and conservation for a discontinuous interface problem. Bit Numer Math 56, 681–704 (2016). https://doi.org/10.1007/s10543-015-0576-7

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  • DOI: https://doi.org/10.1007/s10543-015-0576-7

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