%0 Journal Article
%T A posteriori error estimates for fully discrete fractional-step $\vartheta$-approximations for the heat equation
%A Karakatsani Fotini
%J Mathematics
%D 2014
%I arXiv
%X We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the discretization in space the finite element method with finite element spaces that are allowed to change with time. The first optimal order a posteriori error estimates in $L^\infty(0, T ; L^2({\varOmega}))$ are derived by applying the reconstruction technique.
%U http://arxiv.org/abs/1404.0497v1