Subdiffusion with a time-dependent coefficient: analysis and numerical solution
This work offers rigorous error bounds for numerical solutions of subdiffusion with time-dependent coefficients, benefiting researchers in computational fractional PDEs.
The paper provides a complete error analysis for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, proving optimal-order convergence using a novel perturbation argument. Numerical experiments support the theoretical results.
In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear finite elements in space and backward Euler convolution quadrature in time. The regularity of the solutions of the subdiffusion model is proved for both nonsmooth initial data and incompatible source term. Optimal-order convergence of the numerical solutions is established using the proven solution regularity and a novel perturbation argument via freezing the diffusion coefficient at a fixed time. The analysis is supported by numerical experiments.