  In this paper, we introduce a new global troubled-cell indicator for the
discontinuous Galerkin (DG) method in one- and two-dimensions. This is done by
taking advantage of the global expression of the DG method and re-expanding it
in terms of a multiwavelet basis, which is a sum of the global average and
finer details on different levels. Examining the higher level difference
coefficients acts as a troubled-cell indicator, thus avoiding unnecessary
increased computational cost of a new expansion. In two-dimensions the
multiwavelet decomposition uses combinations of scaling functions and
multiwavelets in the x- and y-directions for improved troubled-cell indication.
By using such a troubled-cell indicator, we are able to reduce the
computational cost by avoiding limiting in smooth regions. We present numerical
examples in one- and two-dimensions and compare our troubled-cell indicator to
the subcell resolution technique of Harten (1989) and the shock detector of
Krivodonova, Xin, Remacle, Chevaugeon, and Flaherty (2004), which were
previously investigated by Qiu and Shu (2005).
