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W. Auzinger:
"Error structures and extrapolation in time for parabolic problems";
in: "Extrapolation and Defect Correction (Bonner Mathematische Schriften, Nr. 228)", H.W. Alt et al. (ed.); issued by: GAMM; GAMM, Bonn, 1991, 41 - 56.

We study asymptotic expansions of the time discretization error for some time stepping schemes applied to (semi-discretizations of) linear parabolic initial/boundary value problems. For this type of problems, the `classical' theory of asymptotic error expansions cannot be applied directly; a more careful analysis is necessary to understand the structure of the time discretization error. We recall and discuss our respective results for the smooth case and present numerical experiments with extrapolation confirming these results. In the final section we discuss the case of nonsmooth solutions caused by inconsistent initial/boundary data.

http://www.math.tuwien.ac.at/~winfried/papers/BONNGAMM90.pdf