| Issue |
ESAIM: M2AN
Volume 58, Number 1, January-February 2024
|
|
|---|---|---|
| Page(s) | 23 - 46 | |
| DOI | https://doi.org/10.1051/m2an/2023100 | |
| Published online | 16 January 2024 | |
A generalized finite element θ-scheme for backward stochastic partial differential equations and its error estimates
School of Mathematics, Shandong University Jinan, Shandong 250100, P.R. China
* Corresponding author: zhaowj@sdu.edu.cn
Received:
1
August
2023
Accepted:
5
December
2023
In this paper, we study numerical methods for solving a class of nonlinear backward stochastic partial differential equations. By utilizing finite element methods in space and θ-scheme in time, the proposed scheme forms a generalized spatio-temporal full discrete scheme, which can be solved in parallel. We rigorously prove the boundedness and error estimates, and obtain the optimal convergence rates in both time (first order/second order) and space (k + 1, k in L2 and H1, respectively). Numerical results are finally provided to demonstrate the effectiveness of the proposed scheme and validate the theoretical analyses.
Mathematics Subject Classification: 65M60 / 60H15 / 60H35 / 65C30
Key words: Backward stochastic partial differential equations / finite element method / θ-scheme error estimates
© The authors. Published by EDP Sciences, SMAI 2024
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