Article ID Journal Published Year Pages File Type
4967072 Journal of Computational Physics 2017 19 Pages PDF
Abstract
In this paper, we consider the Galerkin finite element method for the two-dimensional space and time fractional Bloch-Torrey equation (2D-STFBTE). Utilizing the L2−1σ formula to discretize temporal Caputo derivative, we obtain the local truncation error with O(τ3−α) in the temporal direction, where α is the order of time fractional derivative. Furthermore, the semi-discrete form for the problem is given and, the stability and convergence of the semi-discrete variational formulation are rigorously proved in L2 norm and fractional norm respectively. Then, we derive a fully discrete scheme for the 2D-STFBTE and investigate its convergence theoretically. Finally, extensive numerical results based on linear piecewise polynomials verify the theoretical results and show the effectiveness of the proposed scheme.
Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
Authors
, , , ,