Abstract
We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and discretized in space using a piecewise-linear Galerkin finite element method. The second is continuous in space and employs a time-stepping procedure similar to the classical implicit Euler method. We show that the space discretization is second-order accurate in the spatial L2-norm, uniformly in time, whereas the corresponding error for the time-stepping scheme is O(kα) for a uniform time step k, where α ∈ (1/2, 1) is the fractional diffusion parameter. In numerical experiments using a combined, fully discrete method, we observe convergence behavior consistent with these results.
Original language | English |
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Pages (from-to) | 1763-1784 |
Number of pages | 22 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 54 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jan 2016 |
Externally published | Yes |
Keywords
- Finite elements
- Fractional diffusion
- Gronwall inequality
- Stability
- Time-dependent forcing