  An essential feature of the subdiffusion equations with the $\alpha$-order
time fractional derivative is the weak singularity at the initial time. The
weak regularity of the solution is usually characterized by a regularity
parameter $\sigma\in (0,1)\cup(1,2)$. Under this general regularity assumption,
we here obtain the pointwise-in-time error estimate of the widely used L1
scheme for nonlinear subdiffusion equations. To the end, we present a refined
discrete fractional-type Gr\"onwall inequality and a rigorous analysis for the
truncation errors. Numerical experiments are provided to demonstrate the
effectiveness of our theoretical analysis.
