Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient
arXiv:2310.04246 · doi:10.1016/j.camwa.2024.04.032
Abstract
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.
References in corpus (5)
- Non-diffusive transport in plasma turbulence: a fractional diffusion approach
- Time-stepping error bounds for fractional diffusion problems with non-smooth initial data
- Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications
- Transient superdiffusion and long-range correlations in the motility patterns of trypanosomatid flagellate protozoa
- A linear Galerkin numerical method for a quasilinear subdiffusion equation