A Galerkin finite element method for the modified distributed-order anomalous sub-diffusion equation
Description
In this paper, we consider a modified time distributed-order anomalous sub-diffusion equation for the description of processes becoming less anomalous over the course of time. First, we discretize the integral term using a mid-point quadrature rule and transform the time distributed-order fractional diffusion equation into a multi-term equation. Then applying the backward difference method in time and Galerkin finite element method in space, we present a fully discrete scheme to solve the time distributed-order fractional diffusion equation. Moreover, the stability and convergence of the proposed method are also discussed. Numerical examples are given to verify the accuracy and stability of our scheme.
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| ID Code: | 208863 | ||||||
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| Item Type: | Contribution to Journal (Journal Article) | ||||||
| Refereed: | Yes | ||||||
| ORCID iD: |
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| Additional Information: | Funding Information: Author Li wishes to acknowledge that this research was supported by the National Natural Science Foundation of China (Grant No. 11401223 ), the Science and Technology Program of Guangzhou (No. 201707010031 ) and the China Scholarship Council . Author Liu wishes to acknowledge that this research was partially supported by the Australian Research Council (ARC) via the Discovery Projects ( DP180103858 and DP190101889 ) and National Natural Science Foundation of China (Grant No. 11772046 ). Author Feng wishes to acknowledge that this research was partially supported by the National Natural Science Foundation of China (Grant No. 11801060 ). Author Turner wishes to acknowledge that this research was supported by the Australian Research Council (ARC) via the Discovery Project ( DP180103858 ). | ||||||
| Measurements or Duration: | 18 pages | ||||||
| Additional URLs: | |||||||
| Keywords: | Error analysis, Galerkin finite element method, Stability and convergence, The distributed-order anomalous sub-diffusion equation | ||||||
| DOI: | 10.1016/j.cam.2019.112589 | ||||||
| ISSN: | 0377-0427 | ||||||
| Pure ID: | 76059458 | ||||||
| Divisions: | Past > QUT Faculties & Divisions > Science & Engineering Faculty ?? 3232 ?? |
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| Funding Information: | Author Li wishes to acknowledge that this research was supported by the National Natural Science Foundation of China (Grant No. 11401223 ), the Science and Technology Program of Guangzhou (No. 201707010031 ) and the China Scholarship Council . Author Liu wishes to acknowledge that this research was partially supported by the Australian Research Council (ARC) via the Discovery Projects ( DP180103858 and DP190101889 ) and National Natural Science Foundation of China (Grant No. 11772046 ). Author Feng wishes to acknowledge that this research was partially supported by the National Natural Science Foundation of China (Grant No. 11801060 ). Author Turner wishes to acknowledge that this research was supported by the Australian Research Council (ARC) via the Discovery Project ( DP180103858 ). | ||||||
| Copyright Owner: | 2019 Elsevier B.V. | ||||||
| Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||||||
| Deposited On: | 12 Mar 2021 01:24 | ||||||
| Last Modified: | 29 Feb 2024 11:05 |
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