  We propose a new splitting scheme for general reaction-taxis-diffusion
systems in one spatial dimension capable to deal with simultaneous concentrated
and diffusive regions as well as travelling waves and merging phenomena. The
splitting scheme is based on a mass transport strategy for the cell density
coupled with classical finite element approximations for the rest of the
system. The built-in mass adaption of the scheme allows for an excellent
performance even with respect to dedicated mesh-adapted AMR schemes in original
variables.
