In this study, we construct a space‐time 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...
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https://www.riss.kr/link?id=O105628186
2021년
-
0170-4214
1099-1476
SCIE;SCOPUS
학술저널
2769-2789 [※수록면이 p5 이하이면, Review, Columns, Editor's Note, Abstract 등일 경우가 있습니다.]
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
In this study, we construct a space‐time 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...
In this study, we construct a space‐time 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 associated condition number estimation
1+τnα0h−2γ is derived, where τn and h, respectively, are the current time and space step sizes. Next, we propose a lossless in robustness and adaptive algebraic multigrid (AMG) with
O(MlogM) computational cost and
O(M) matrix‐free storage, in contrast to classical AMG with
O(M2), where M is the number of spatial segments. Meanwhile, uniform convergence analyses on the two‐level V(0,1)‐cycle of classical and adaptive AMGs are provided. Finally, we demonstrate the optimal error order of space‐time FE approximations in the L2(Ω) norm sense, present theoretical confirmations and predictable behaviors of the proposed algorithm in numerical experiments.
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