A drift-randomized Milstein–Galerkin finite element method for semilinear stochastic evolution equations

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Qi, Xiao and Wu, Yue and Yan, Yubin (2027) A drift-randomized Milstein–Galerkin finite element method for semilinear stochastic evolution equations. Applied Numerical Mathematics, 231. 70 - 85. ISSN 0168-9274 (https://doi.org/10.1016/j.apnum.2026.09.009)

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Abstract

Kruse and Wu [Math. Comp. 88 (2019) 2793–2825] proposed a fully discrete randomized Galerkin finite element method for semilinear stochastic evolution equations (SEEs) driven by additive noise and showed that this method attains a temporal strong convergence rate exceeding order 1/2 without imposing any differentiability assumptions on the drift nonlinearity. They further discussed a potential extension of the randomized method to SEEs with multiplicative noise and introduced the so-called drift-randomized Milstein–Galerkin finite element fully discrete scheme, but without providing a corresponding strong convergence analysis. This paper aims to fill this gap by rigorously analyzing the strong convergence behavior of the drift-randomized Milstein-Galerkin finite element scheme. By avoiding the use of differentiability assumptions on the nonlinear drift term, we establish strong convergence rates in both space and time for the proposed method. The obtained temporal convergence result is ⁡(Δ⁢1−0), where Δt denotes the time step size and ε0 is an arbitrarily small positive number. Numerical experiments are reported to validate the theoretical findings.

ORCID iDs

Qi, Xiao, Wu, Yue ORCID logoORCID: https://orcid.org/0000-0002-6281-2229 and Yan, Yubin;
  • Item type:Article
    ID code:97380
    Dates:
    Date
    Event
    1 January 2027
    Published
    17 September 2026
    Published Online
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:02 Oct 2026 10:47
    Last modified:03 Oct 2026 07:08
    URI:https://strathprints.strath.ac.uk/id/eprint/97380
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