  We shall develop a fully discrete space-time adaptive method for linear
parabolic problems based on new reliable and efficient a posteriori analysis
for higher order dG(s) finite element discretisations. The adaptive strategy is
motivated by the principle of equally distributing the a posteriori indicators
in time and the convergence of the method is guaranteed by the uniform energy
estimate from [KreuzerM\"ollerSchmidtSiebert:12] under minimal assumptions on
the regularity of the data.
