TY - JOUR
T1 - Finite Element Methods for Nonlinear Backward Stochastic Partial Differential Equations and Their Error Estimates
AU - Yang , Xu
AU - Zhao , Weidong
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1457
EP - 1480
PY - 2020
DA - 2020/09
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0345
UR - https://global-sci.org/intro/article_detail/aamm/18296.html
KW - Backward stochastic partial differential equations, finite element method, error estimate.
AB - <p style="text-align: justify;">In this paper, we consider numerical approximation of a class of nonlinear backward stochastic partial differential equations (BSPDEs). By using finite element methods in the physical space domain and the Euler method in the time domain, we propose a spatial finite element semi-discrete scheme and a spatio-temporal full discrete scheme for solving the BSPDEs. Errors of the schemes are rigorously analyzed and theoretical error estimates with convergence rates are obtained.</p>