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Subdiffusion with Time-Dependent Coefficients: Improved Regularity and Second-Order Time Stepping

Jin, B; Li, B; Zhou, Z; (2020) Subdiffusion with Time-Dependent Coefficients: Improved Regularity and Second-Order Time Stepping. Numerische Mathematik , 145 pp. 883-913. 10.1007/s00211-020-01130-2. Green open access

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Abstract

This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with time-dependent coefficients. Using these regularity results and a perturbation argument of freezing the diffusion coefficient, we prove that the convolution quadrature generated by the second-order backward differentiation formula, with proper correction at the first time step, can achieve second-order convergence for both nonsmooth initial data and incompatible source term. Numerical experiments are consistent with the theoretical results.

Type: Article
Title: Subdiffusion with Time-Dependent Coefficients: Improved Regularity and Second-Order Time Stepping
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00211-020-01130-2
Publisher version: https://doi.org/10.1007/s00211-020-01130-2
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10099691
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