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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Subdiffusion with a time-dependent coefficient: Analysis and numerical solution
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by Bangti Jin, Buyang Li and Zhi Zhou HTML | PDF
Math. Comp. 88 (2019), 2157-2186 Request permission

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.
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Additional Information
  • Bangti Jin
  • Affiliation: Department of Computer Science, University College London, Gower Street, London WC1E 6BT, United Kingdom
  • MR Author ID: 741824
  • Email: bangti.jin@gmail.com, b.jin@ucl.ac.uk
  • Buyang Li
  • Affiliation: Department of Applied Mathematics, The Polytechnic University of Hong Kong, Kowloon, Hong Kong
  • MR Author ID: 910552
  • Email: bygli@polyu.edu.hk
  • Zhi Zhou
  • Affiliation: Department of Applied Mathematics, The Polytechnic University of Hong Kong, Kowloon, Hong Kong
  • MR Author ID: 1011798
  • Email: zhizhou@polyu.edu.hk
  • Received by editor(s): April 17, 2018
  • Received by editor(s) in revised form: September 10, 2018
  • Published electronically: February 6, 2019
  • Additional Notes: The research of the second author was partially supported by a Hong Kong RGC grant (Project No. 15300817).
    The research of the third author was supported by a start-up grant from the Hong Kong Polytechnic University and Hong Kong RGC grant No. 25300818.
  • © Copyright 2019 American Mathematical Society
  • Journal: Math. Comp. 88 (2019), 2157-2186
  • MSC (2010): Primary 65M30, 65M15, 65M12
  • DOI: https://doi.org/10.1090/mcom/3413
  • MathSciNet review: 3957890