Pointwise-in-time a posteriori error control for time-fractional parabolic equations

For time-fractional parabolic equations with a Caputo time derivative of order α ∈ (0, 1), we give pointwise-in-time a posteriori error bounds in the spatial L2 and L∞ norms. Hence, an adaptive mesh construction algorithm is applied for the L1 method, which yields optimal convergence rates 2 − α in the presence of solution singularities