@Article{CSIAM-AM-6-1,
author = {Yongwang, Sun and Zhao, Weidong and Zhao, Wenju},
title = {Error Estimates of Finite Element Methods for the Nonlinear Backward Stochastic Stokes Equations},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2025},
volume = {6},
number = {1},
pages = {31--62},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2024-0021},
url = {https://global-sci.com/article/91667/error-estimates-of-finite-element-methods-for-the-nonlinear-backward-stochastic-stokes-equations}
}