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Mathematics > Numerical Analysis

arXiv:1809.07583 (math)
[Submitted on 20 Sep 2018 (v1), last revised 21 Sep 2018 (this version, v2)]

Title:Subdiffusion with a time-dependent coefficient: analysis and numerical solution

Authors:Bangti Jin, Buyang Li, Zhi Zhou
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Abstract:In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear finite elements in space and backward Euler convolution quadrature in time. The regularity of the solutions of the subdiffusion model is proved for both nonsmooth initial data and incompatible source term. Optimal-order convergence of the numerical solutions is established using the proven solution regularity and a novel perturbation argument via freezing the diffusion coefficient at a fixed time. The analysis is supported by numerical experiments.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1809.07583 [math.NA]
  (or arXiv:1809.07583v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1809.07583

Submission history

From: Buyang Li [view email]
[v1] Thu, 20 Sep 2018 12:04:26 UTC (22 KB)
[v2] Fri, 21 Sep 2018 00:33:27 UTC (24 KB)
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