Well-Posedness, Stability and Conservation for a Discontinuous Interface Problem: An Initial Investigation
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.
KeywordsJump Condition Advection Equation Advection Velocity Penalty Coefficient Discontinuous Coefficient
- 8.C. La Cognata, J. Nordström, Well-Posedness, Stability and Conservation for a Discontinuous Interface Problem. LiTH-MAT-R–2014/16–SE, Department of Mathematics, Linköping University, 2014Google Scholar