  We present a new numerical scheme which combines the Spectral Difference (SD)
method up to arbitrary high order with \emph{a-posteriori} limiting using the
classical MUSCL-Hancock scheme as fallback scheme. It delivers very accurate
solutions in smooth regions of the flow, while capturing sharp discontinuities
without spurious oscillations. We exploit the strict equivalence between the SD
scheme and a Finite-Volume (FV) scheme based on the SD control volumes to
enable a straightforward limiting strategy. At the end of each stage of our
high-order time-integration ADER scheme, we check if the high-order solution is
admissible under a number of numerical and physical criteria. If not, we
replace the high-order fluxes of the troubled cells by fluxes from our robust
second-order MUSCL fallback scheme. We apply our method to a suite of test
problems for the 1D and 2D Euler equations. We demonstrate that this
combination of SD and ADER provides a virtually arbitrary high order of
accuracy, while at the same time preserving good sub-element shock capturing
capabilities.
