  In this article, we present an extension of the splitting algorithm proposed
in [22] to networks of conservation laws with piecewise linear discontinuous
flux functions in the unknown. We start with the discussion of a suitable
Riemann solver at the junction and then describe a strategy how to use the
splitting algorithm on the network. In particular, we focus on two types of
junctions, i.e., junctions where the number of outgoing roads does not exceed
the number of incoming roads (dispersing type) and junctions with two incoming
and one outgoing road (merging type). Finally, numerical examples demonstrate
the accuracy of the splitting algorithm by comparisons to the exact solution
and other approaches used in the literature.
