Jin, B;
Lazarov, R;
Sheen, D;
Zhou, Z;
(2016)
Error Estimates for Approximations of Distributed Order Time Fractional Diffusion with Nonsmooth Data.
Journal of Fractional Calculus and Applied Analysis
, 19
(1)
pp. 69-93.
10.1515/fca-2016-0005.
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Abstract
In this work, we consider the numerical solution of a distributed order subdiffusion model, arising in the modeling of ultra-slow diffusion processes. We develop a space semidiscrete scheme based on the Galerkin finite element method, and establish error estimates optimal with respect to data regularity in L2(Ω) and H1(Ω) norms for both smooth and nonsmooth initial data. Further, we propose two fully discrete schemes, based on the Laplace transform and convolution quadrature generated by the backward Euler method, respectively, and provide optimal L2(Ω) error estimates, which exhibits exponential convergence and first-order convergence in time, respectively. Extensive numerical experiments are provided to verify the error estimates for both smooth and nonsmooth initial data.
| Type: | Article |
|---|---|
| Title: | Error Estimates for Approximations of Distributed Order Time Fractional Diffusion with Nonsmooth Data |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1515/fca-2016-0005 |
| Publisher version: | http://dx.doi.org/10.1515/fca-2016-0005 |
| Additional information: | Copyright © 2016 by Walter de Gruyter GmbH. |
| Keywords: | distributed order; fractional diffusion; Galerkin finite element method; fully discrete scheme; error estimates |
| 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-pp.ucl.ac.uk/id/eprint/1472782 |
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