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

A convergent time-space adaptive dG(s) finite element method for parabolic problems motivated by equal error distribution