Finite Element Methods for Nonlinear Backward Stochastic Partial Differential Equations and Their Error Estimates (Advances in Applied Mathematics and Mechanics, 2021)
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.