“…A posteriori error estimators for finite element discretizations of nonlinear parabolic problems are available in the literature (e.g., [5,6,7,11,14,24,31,46,47,48]). However, the literature on a posteriori error control for parabolic equations that exhibit finite time blow-up is very limited; to the best of our knowledge, only in [33] do the authors provide rigorous a posteriori error bounds for such problems. Using a semigroup approach, the authors of [33] arrive to conditional a posteriori error estimates in the L ∞ (L ∞ )-norm for first and second order temporal semi-discretizations of a semilinear parabolic equation with polynomial nonlinearity.…”