Time-space Finite Element Adaptive AMG for Multi-term Time Fractional Advection Diffusion Equations

2017/08/07 by Xiaoqiang Yue, Yehong Xu, Yue, Xiaoqiang +7
Engineering · Mathematics · #35R11 #65F10 #65F15 #65N55 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1708.02126

openalex publication_date 2017/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this study we construct a time-space finite element (FE) scheme and furnish cost-efficient approximations for one-dimensional multi-term time fractional advection diffusion equations on a bounded domain Ω. Firstly, a fully discrete scheme is obtained by the linear FE method in both temporal and spatial directions, and many characterizations on the resulting matrix are established. Secondly, the condition number estimation is proved, an adaptive algebraic multigrid (AMG) method is further developed to lessen computational cost and analyzed in the classical framework. Finally, some numerical experiments are implemented to reach the saturation error order in the L²(Ω) norm sense, and present theoretical confirmations and predictable behaviors of the proposed algorithm.

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