Alternating Direction Implicit Galerkin Finite Element Method for the Two-Dimensional Time Fractional Evolution Equation
Year: 2014
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 1 : pp. 41–57
Abstract
New numerical techniques are presented for the solution of the two-dimensional time fractional evolution equation in the unit square. In these methods, Galerkin finite element is used for the spatial discretization, and, for the time stepping, new alternating direction implicit (ADI) method based on the backward Euler method combined with the first order convolution quadrature approximating the integral term are considered. The ADI Galerkin finite element method is proved to be convergent in time and in the $L^2$ norm in space. The convergence order is $\mathcal{O}$($k$|ln $k$|+$h^r$), where $k$ is the temporal grid size and $h$ is spatial grid size in the $x$ and $y$ directions, respectively. Numerical results are presented to support our theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2014.y11051
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 1 : pp. 41–57
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Fractional evolution equation alternating direction implicit method Galerkin finite element method backward Euler.
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