| Abstract: | ![]()
New numerical techniques are presented for the solution of thetwo-dimensional time fractional evolution equation in the unitsquare. In these methods, Galerkin finite element is used for thespatial discretization, and, for the time stepping, new alternatingdirection implicit (ADI) method based on the backward Euler methodcombined with the first order convolution quadrature approximatingthe integral term are considered. The ADI Galerkin finite elementmethod is proved to be convergent in time and in the $L^2$ norm inspace. The convergence order is$mathcal{O}$($k$|ln $k$|+$h^r$), where $k$ isthe temporal grid size and $h$ is spatial grid size in the $x$ and $y$ directions, respectively. Numerical results are presented tosupport our theoretical analysis. |
