K. Eriksson, C. Johnson, and S. Larsson,

Adaptive finite element methods for parabolic problems. VI.
Analytic semigroups,

SIAM J. Numer. Anal. 35 (1998), 1315-1325
http://epubs.siam.org/sam-bin/dbq/article/31021

Abstract. 
  We continue our work on adaptive finite element methods with a study
  of time discretization of analytic semigroups.  We prove optimal
  apriori and aposteriori error estimates for the discontinuous
  Galerkin method showing, in particular, that analytic semigroups
  allow long-time integration without error accumulation.

Keywords.  Analytic semigroup, parabolic problem, discontinuous
  Galerkin method, error estimate, a priori, a posteriori, strong
  stability.