Numerical solution of nonstationary problems for a space-fractional diffusion equation
This work provides a computational approach for time-dependent fractional diffusion equations, which is incremental for researchers in numerical PDEs.
The paper develops a numerical method for solving nonstationary space-fractional diffusion equations using finite element spatial discretization and regularized two-level time schemes, with numerical results for a 2D model problem.
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary conditions of Robin type. Finite element approximation in space is employed. To construct approximation in time, regularized two-level schemes are used. The numerical implementation is based on solving the equation with the fractional power of the elliptic operator using an auxiliary Cauchy problem for a pseudo-parabolic equation. The results of numerical experiments are presented for a model two-dimensional problem.