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

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    Authors
    Yan, Yubin
    Kang, Wenyan
    Egwu, Bernard
    Pani, Amiya K.
    Affiliation
    Lvliang University; University of Chester; Indian Institute of Technology Bombay
    Publication Date
    2021-05-21
    
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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
    URI
    http://hdl.handle.net/10034/625115
    DOI
    10.1093/imanum/drab035
    Additional Links
    https://academic.oup.com/imajna/advance-article-abstract/doi/10.1093/imanum/drab035/6278467?redirectedFrom=fulltext
    Type
    Article
    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
    ISSN
    0272-4979
    EISSN
    1464-3642
    ae974a485f413a2113503eed53cd6c53
    10.1093/imanum/drab035
    Scopus Count
    Collections
    Mathematics

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