  The cost- and memory-efficient numerical simulation of coupled volume-based
multi-physics problems like flow, transport, wave propagation and others
remains a challenging task with finite element method (FEM) approaches.
Goal-oriented space and time adaptive methods derived from the dual weighted
residual (DWR) method appear to be a shiny key technology to generate optimal
space-time meshes to minimise costs. Current implementations for challenging
problems of numerical screening tools including the DWR technology broadly
suffer in their extensibility to other problems, in high memory consumption or
in missing system solver technologies. This work contributes to the efficient
embedding of DWR space-time adaptive methods into numerical screening tools for
challenging problems of physically relevance with a new approach of flexible
data structures and algorithms on them, a modularised and complete
implementation as well as illustrative examples to show the performance and
efficiency.
