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Alternating Direction Implicit Galerkin Finite Element Method for the Two-Dimensional Time Fractional Evolution Equation

Published online by Cambridge University Press:  28 May 2015

Limei Li and
Da Xu
Limei Li*
Affiliation:
College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, ChinaDepartment of Mathematics, Hunan Institute of Science and Technology, Yueyang 414000, China
Da Xu*
Affiliation:
College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China
*
Corresponding author.Email address:limeiliyy@163.com
Corresponding author.Email address:daxu@hunnu.edu.cn
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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 𝓞(k|ln k| + hr ), 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.

Keywords

65M0665M1265M1565M60Fractional evolution equationalternating direction implicit methodGalerkin finite element methodbackward Euler

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 1 , February 2014, pp. 41 - 57
Copyright
Copyright © Global Science Press Limited 2014

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