A convergent time-space adaptive dG(s) finite element method for   parabolic problems motivated by equal error distribution
  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. 
Fernando Gaspoz and Christian Kreuzer and Kunibert Siebert and Daniel   Ziegler
math.NA