A Posteriori Error Estimates for the Fractional–step Θ-scheme for Linear Parabolic Equations

We derive residual-based a posteriori error estimates of optimal order for time discretizations by the fractional-step θ-scheme for linear parabolic equations. First, we consider the time semi-discrete problem. The main tool of our analysis is an appropriate reconstruction of the piecewise linear interpolant of the approximate solution that leads to a residual of optimal order. Next, we extend the above mentioned results to the case of full discretization. The theoretical results are justified with numerical experiments.