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Mathematics > Numerical Analysis

arXiv:2106.03100 (math)
[Submitted on 6 Jun 2021]

Title:Optimal error estimation of a time-spectral method for fractional diffusion problems with low regularity data

Authors:Hao Luo, Xiaoping Xie
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Abstract:This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the Besov space are established. A time-spectral algorithm is developed which adopts a standard spectral method and a conforming linear finite element method for temporal and spatial discretizations, respectively. Optimal error estimates are derived with nonsmooth data. Particularly, a sharp temporal convergence rate $1+2\alpha$ is shown theoretically and numerically.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2106.03100 [math.NA]
  (or arXiv:2106.03100v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2106.03100

Submission history

From: Xiaoping Xie [view email]
[v1] Sun, 6 Jun 2021 12:02:13 UTC (1,002 KB)
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