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Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise

Yan, Yubin
; 
Kang, Wenyan
; 
Egwu, Bernard
; 
Pani, Amiya K.
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Affiliation
Lvliang University; University of Chester; Indian Institute of Technology Bombay
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Publication Date
2021-05-21
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Mathematics
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Abstract
A Galerkin finite element method is applied to approximate the solution of a semilinear stochastic space and time fractional subdiffusion problem with the Caputo fractional derivative of the order $ \alpha \in (0, 1)$, driven by fractionally integrated additive noise. After discussing the existence, uniqueness and regularity results, we approximate the noise with the piecewise constant function in time in order to obtain a regularized stochastic fractional subdiffusion problem. The regularized problem is then approximated by using the finite element method in spatial direction. The mean squared errors are proved based on the sharp estimates of the various Mittag-Leffler functions involved in the integrals. Numerical experiments are conducted to show that the numerical results are consistent with the theoretical findings.
Citation
Kang, W., Egwu, B. A., Yan, Y., Pani, A. K. (2022). Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise. IMA Journal of Numerical Analysis, 42(3), 2301–2335. https://doi.org/10.1093/imanum/drab035
Publisher
Oxford University Press
Journal
IMA Journal of Numerical Analysis
Research Unit
URI
http://hdl.handle.net/10034/625115
DOI
10.1093/imanum/drab035
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PubMed Central ID
Type
Article
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Description
This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record Kang, W., Egwu, B. A., Yan, Y., Pani, A. K. (2022). Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise. IMA Journal of Numerical Analysis, 42(3), 2301–2335 is available online at: https://doi.org/10.1093/imanum/drab035
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ISSN
0272-4979
EISSN
1464-3642
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https://academic.oup.com/imajna/advance-article-abstract/doi/10.1093/imanum/drab035/6278467?redirectedFrom=fulltext