  In Vuik and Ryan (2014) we studied the use of troubled-cell indicators for
discontinuity detection in nonlinear hyperbolic partial differential equations
and introduced a new multiwavelet technique to detect troubled cells. We found
that these methods perform well as long as a suitable, problem-dependent
parameter is chosen. This parameter is used in a threshold which decides
whether or not to detect an element as a troubled cell. Until now, these
parameters could not be chosen automatically. The choice of the parameter has
impact on the approximation: it determines the strictness of the troubled-cell
indicator. An inappropriate choice of the parameter will result in detection
(and limiting) of too few or too many elements. The optimal parameter is chosen
such that the minimal number of troubled cells is detected and the resulting
approximation is free of spurious oscillations. In this paper we will see that
for each troubled-cell indicator the sudden increase or decrease of the
indicator value with respect to the neighboring values is important for
detection. Indication basically reduces to detecting the outliers of a vector
(one dimension) or matrix (two dimensions). This is done using Tukey's boxplot
approach to detect which coefficients in a vector are straying far beyond
others (Tukey, 1977). We provide an algorithm that can be applied to various
troubled-cell indication variables. Using this technique the problem-dependent
parameter that the original indicator requires is no longer necessary as the
parameter will be chosen automatically.
