Error Estimates of Finite Element Methods for the Nonlinear Backward Stochastic Stokes Equations
Year: 2025
Author: Yongwang Sun, Weidong Zhao, Wenju Zhao
CSIAM Transactions on Applied Mathematics, Vol. 6 (2025), Iss. 1 : pp. 31–62
Abstract
This paper is concerned with the numerical analyses of finite element methods for the nonlinear backward stochastic Stokes equations (BSSEs) where the forcing term is coupled with z. Under several developed analysis techniques, the error estimates of the proposed semi-discrete and fully discrete schemes, as well as their boundedness, are rigorously presented and established. Optimal convergence rates of the fully discrete scheme are obtained not only for the velocity u and auxiliary stochastic process z but also for the pressure p. For the efficiency of solving BSSEs, the proposed numerical scheme is parallelly designed in stochastic space. Numerical results are finally provided and tested in parallel to validate the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2024-0021
CSIAM Transactions on Applied Mathematics, Vol. 6 (2025), Iss. 1 : pp. 31–62
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Backward stochastic Stokes equations variational methods finite element method error estimates.
Author Details
Yongwang Sun Email
Weidong Zhao Email
Wenju Zhao Email