@Article{AAMM-10-5,
author = {Yue, X., Q. and W., P., Bu and Shu, S. and M., Liu, H. and Wang, S.},
title = {Fully Finite Element Adaptive AMG Method for Time-Space Caputo-Riesz Fractional Diffusion Equations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {10},
number = {5},
pages = {1103--1125},
abstract = {<p style="text-align: justify;">The paper aims to establish a fully discrete finite element (FE) scheme and
provide cost-effective solutions for one-dimensional time-space Caputo-Riesz fractional
diffusion equations on a bounded domain $Ω$. Firstly, we construct a fully discrete
scheme of the linear FE method in both temporal and spatial directions, derive
many characterizations on the coefficient matrix and numerically verify that the fully
discrete FE approximation possesses the saturation error order under&nbsp;$L^2(Ω)$ norm.
Secondly, we theoretically prove the estimation $1+\mathcal{O}(τ^αh^{−2β})$ on the condition number
of the coefficient matrix, in which $τ$ and $h$ respectively denote time and space
step sizes. Finally, on the grounds of the estimation and fast Fourier transform, we
develop and analyze an adaptive algebraic multigrid (AMG) method with low algorithmic
complexity, reveal a reference formula to measure the strength-of-connection
tolerance which severely affect the robustness of AMG methods in handling fractional
diffusion equations, and illustrate the well robustness and high efficiency of the proposed
algorithm compared with the classical AMG, conjugate gradient and Jacobi iterative
methods.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2018-0046},
url = {https://global-sci.com/article/73215/fully-finite-element-adaptive-amg-method-for-time-space-caputo-riesz-fractional-diffusion-equations}
}