Pointwise-in-time a posteriori error control for time-fractional parabolic equations

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Abstract

For time-fractional parabolic equations with a Caputo time derivative of order α∈(0,1), we give pointwise-in-time a posteriori error bounds in the spatial L2 and L norms. Hence, an adaptive mesh construction algorithm is applied for the L1 method, which yields optimal convergence rates 2−α in the presence of solution singularities.

Original languageEnglish
Article number107515
JournalApplied Mathematics Letters
Volume123
DOIs
Publication statusPublished - Jan 2022

Keywords

  • Fractional-order parabolic equation
  • Graded meshes
  • L1 scheme
  • Optimal convergence rates
  • Pointwise-in-time a posteriori error bounds

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