Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4638409 | Journal of Computational and Applied Mathematics | 2015 | 10 Pages |
Abstract
The numerical solution of a space–time fractional diffusion equation used to model the anomalous diffusion is considered. Spatial discretization is effected using a finite element method whereas the θθ-scheme is used for temporal discretization. The fully discrete scheme is analyzed for all 0≤θ≤10≤θ≤1 to determine conditional and unconditional stability regimes for the scheme and also to obtain error estimates for the approximate solution. The analysis is facilitated by making use of a variational formulation of the equations that is based on a recently developed nonlocal calculus. One-dimensional numerical examples are provided that illustrate the theoretical stability and convergence results.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Qingguang Guan, Max Gunzburger,