  We consider goal-oriented adaptive space-time finite-element discretizations
of the parabolic heat equation on completely unstructured simplicial space-time
meshes. In some applications, we are interested in an accurate computation of
some possibly nonlinear functionals at the solution, so called goal
functionals. This motivates the use of adaptive mesh refinements driven by the
dual-weighted residual (DWR) method. The DWR method requires the numerical
solution of a linear adjoint problem that provides the sensitivities for the
mesh refinement. This can be done by means of the same full space-time finite
element discretization as used for the primal linear problem. The numerical
experiment presented demonstrates that this goal-oriented, full space-time
finite element solver efficiently provides accurate numerical results for a
model problem with moving domains and a linear goal functional, where we know
the exact value.
