Subdiffusion with time-dependent coefficients: improved regularity and second-order time stepping

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 perturb...

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Bibliographic Details
Published in:Numerische Mathematik 2020-08, Vol.145 (4), p.883-913
Main Authors: Jin, Bangti, Li, Buyang, Zhou, Zhi
Format: Article
Language:English
Subjects:
Convolution
Diffusion coefficient
Freezing
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Perturbation
Quadratures
Regularity
Simulation
Theoretical
Time dependence
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Summary: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.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-020-01130-2