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Incomplete Iterative Solution of the Subdiffusion Problem

Jin, B; Zhou, Z; (2020) Incomplete Iterative Solution of the Subdiffusion Problem. Numerische Mathematik , 145 pp. 693-725. 10.1007/s00211-020-01128-w. Green open access

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Abstract

In this work, we develop an efficient incomplete iterative scheme for the numerical solution of the subdiffusion model involving a Caputo derivative of order α∈(0,1) in time. It is based on piecewise linear Galerkin finite element method in space and backward Euler convolution quadrature in time and solves one linear algebraic system inexactly by an iterative algorithm at each time step. We present theoretical results for both smooth and nonsmooth solutions, using novel weighted estimates of the time-stepping scheme. The analysis indicates that with the number of iterations at each time level chosen properly, the error estimates are nearly identical with that for the exact linear solver, and the theoretical findings provide guidelines on the choice. Illustrative numerical results are presented to complement the theoretical analysis.

Type: Article
Title: Incomplete Iterative Solution of the Subdiffusion Problem
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00211-020-01128-w
Publisher version: https://doi.org/10.1007/s00211-020-01128-w
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 > 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/10100831
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