A superconvergent stencil-adaptive SBP-SAT finite difference scheme

A stencil-adaptive SBP-SAT finite difference scheme is shown to display superconvergent behavior. Applied to the linear advection equation, it has a convergence rate $\mathcal{O}(\mathrm{\Delta }{x}^4)$ in contrast to a conventional scheme, which converges at a rate $\mathcal{O}(\mathrm{\Delta }{x}^3)$.