For time-fractional parabolic equations with a Caputo time derivative of order \(\alpha\in(0,1)\), we give pointwise-in-time a posteriori error bounds in the spatial \(L_2\) and \(L_\infty\) norms. Hence, an adaptive mesh construction algorithm is applied for the L1 method, which yields optimal convergence rates \(2-\alpha\) in the presence of solution singularities.

The talk is based on the recent article: N. Kopteva, Pointwise-in-time a posteriori error control for time-fractional parabolic equations, Appl. Math. Lett., 2021, https://doi.org/10.1016/j.aml.2021.107515.