We couple the L1 discretization of the Caputo fractional derivative in time with the Galerkin scheme to devise a linear numerical method for the semilinear subdiffusion equation. Two important points that we make are: nonsmooth initial data and time-dependent diffusion coefficient. We prove the stability and convergence of the method under weak assumptions concerning regularity of the diffusivity. We find optimal pointwise in space and global in time errors, which are verified with several numerical experiments.

翻译：我们将Caputo分数阶导数的时间L1离散化与Galerkin格式耦合，为半线性次扩散方程设计了一种线性数值方法。本文的两个重要关注点在于：非光滑初始数据和时变扩散系数。我们在关于扩散系数正则性的弱假设下，证明了该方法的稳定性和收敛性。我们得到了空间逐点最优且时间全局的误差估计，并通过多个数值实验进行了验证。