TY - JOUR
T1 - Error Estimates of Finite Element Methods for the Nonlinear Backward Stochastic Stokes Equations
AU - Sun , Yongwang
AU - Zhao , Weidong
AU - Zhao , Wenju
JO - CSIAM Transactions on Applied Mathematics
VL - 1
SP - 31
EP - 62
PY - 2025
DA - 2025/02
SN - 6
DO - http://doi.org/10.4208/csiam-am.SO-2024-0021
UR - https://global-sci.org/intro/article_detail/csiam-am/23795.html
KW - Backward stochastic Stokes equations, variational methods, finite element method, error estimates.
AB - <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>