Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise

Tambue A, Mukam JD (2023)
Results in Applied Mathematics 17: 100351.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Tambue, Antoine; Mukam, Jean DanielUniBi
Abstract / Bemerkung
This paper aims to investigate the finite element weak convergence rate for semilinear parabolic stochastic partial differential equations(SPDEs) driven by additive noise. In contrast to many results in the current scientific literature, we investigate the more general case where the nonlinearity is allowed to be of Nemytskii-type and the linear operator is not necessarily self-adjoint, which is more challenging and models more realistic phenomena such as convection–reaction–diffusion processes. Using Malliavin calculus, Kolmogorov equations and by splitting the linear operator into a self-adjoint and non self-adjoint parts, we prove the convergence of the finite element approximation and obtain a weak convergence rate that is twice the strong convergence rate.
Stichworte
Semilinear parabolic partial differential equations Finite element method Weak convergence Additive noise
Erscheinungsjahr
2023
Zeitschriftentitel
Results in Applied Mathematics
Band
17
Art.-Nr.
100351
ISSN
25900374
Page URI
https://pub.uni-bielefeld.de/record/2968036

Zitieren

Tambue A, Mukam JD. Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise. Results in Applied Mathematics. 2023;17: 100351.
Tambue, A., & Mukam, J. D. (2023). Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise. Results in Applied Mathematics, 17, 100351. https://doi.org/10.1016/j.rinam.2022.100351
Tambue, Antoine, and Mukam, Jean Daniel. 2023. “Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise”. Results in Applied Mathematics 17: 100351.
Tambue, A., and Mukam, J. D. (2023). Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise. Results in Applied Mathematics 17:100351.
Tambue, A., & Mukam, J.D., 2023. Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise. Results in Applied Mathematics, 17: 100351.
A. Tambue and J.D. Mukam, “Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise”, Results in Applied Mathematics, vol. 17, 2023, : 100351.
Tambue, A., Mukam, J.D.: Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise. Results in Applied Mathematics. 17, : 100351 (2023).
Tambue, Antoine, and Mukam, Jean Daniel. “Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise”. Results in Applied Mathematics 17 (2023): 100351.
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