Well-Posedness, Stability and Conservation for a Discontinuous Interface Problem: An Initial Investigation
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- La Cognata C., Nordström J. (2015) Well-Posedness, Stability and Conservation for a Discontinuous Interface Problem: An Initial Investigation. In: Kirby R., Berzins M., Hesthaven J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham
A robust interface treatment for the discontinuous coefficient advection equation satisfying time-independent jump conditions is presented. The aim of the investigation is to show how the different concepts like well-posedness, conservation and stability are related. The equations are discretized using high order finite difference methods on Summation By Parts (SBP) form. The interface conditions are weakly imposed using the Simultaneous Approximation Term (SAT) procedure. Spectral analysis and numerical simulations corroborate the theoretical findings.