A Finite Element Approximation for a Class of Caputo Time-Fractional Diffusion Equations
This work provides a numerical method for solving time-fractional diffusion equations, which is incremental as it applies existing techniques to a specific class of problems.
The authors developed a fully discrete scheme combining finite difference in time and finite element in space for Caputo time-fractional diffusion equations, deriving stability and error estimates, and demonstrating accuracy through two numerical examples.
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates are derived. The accuracy and efficiency of the presented method is shown by conducting two numerical examples.