Abstract: Parabolic equations with delay has been widely appeared in scientific and engineering fields.In this  paper we consider the time approximation of parabolic equations with delay.Firstly,we prove the stability of  variable step-size BDF2method for parabolic equations with delay.Then,we derive a higher order numerical  approximation by reconstruction.Finally,we obtain a posteriori estimates of variable step-size BDF2 method for the equations.

Key words: Parabolic equation with delay； Stability analysis； Reconstruction； Posteriori error estimate； , BDF method