A generalized finite element θ-scheme for backward stochastic partial differential equations and its error estimates

被引：0

作者：

Sun, Yongwang ^{[1
]}

Zhao, Weidong ^{[1
]}

Zhao, Wenju ^{[1
]}

机构：

[1] Shandong Univ Jinan, Sch Math, Jinan 250100, Shandong, Peoples R China

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS | 2024年 / 58卷 / 01期

关键词：

Backward stochastic partial differential equations; finite element method; theta-scheme error estimates; ADAPTED SOLUTION;

D O I：

10.1051/m2an/2023100

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study numerical methods for solving a class of nonlinear backward stochastic partial differential equations. By utilizing finite element methods in space and theta-scheme in time, the proposed scheme forms a generalized spatio-temporal full discrete scheme, which can be solved in parallel. We rigorously prove the boundedness and error estimates, and obtain the optimal convergence rates in both time (first order/second order) and space (k + 1, k in L-2 and H-1, respectively). Numerical results are finally provided to demonstrate the effectiveness of the proposed scheme and validate the theoretical analyses.

引用

页码：23 / 46

页数：24

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