  This work reviews goal-oriented a posteriori error control, adaptivity and
solver control for finite element approximations to boundary and
initial-boundary value problems for stationary and non-stationary partial
differential equations, respectively. In particular, coupled field problems
with different physics may require simultaneously the accurate evaluation of
several quantities of interest, which is achieved with multi-goal oriented
error control. Sensitivity measures are obtained by solving an adjoint problem.
Error localization is achieved with the help of a partition-of-unity. We also
review and extend theoretical results for efficiency and reliability by
employing a saturation assumption. The resulting adaptive algorithms allow to
balance discretization and non-linear iteration errors, and are demonstrated
for four applications: Poisson's problem, non-linear elliptic boundary value
problems, stationary incompressible Navier-Stokes equations, and regularized
parabolic $p$-Laplace initial-boundary value problems. Therein, different
finite element discretizations in two different software libraries are
utilized, which are partially accompanied with open-source implementations on
GitHub.
