Volume 12, Issue 6
Finite Element Methods for Nonlinear Backward Stochastic Partial Differential Equations and Their Error Estimates

Xu Yang & Weidong Zhao

Adv. Appl. Math. Mech., 12 (2020), pp. 1457-1480.

Published online: 2020-09

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  • Abstract

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.

  • Keywords

Backward stochastic partial differential equations, finite element method, error estimate.

  • AMS Subject Headings

60H15, 60H35, 65C30, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-12-1457, author = {Yang , Xu and Zhao , Weidong}, title = {Finite Element Methods for Nonlinear Backward Stochastic Partial Differential Equations and Their Error Estimates}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {6}, pages = {1457--1480}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0345}, url = {http://global-sci.org/intro/article_detail/aamm/18296.html} }
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 -

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.

Xu Yang & Weidong Zhao. (2020). Finite Element Methods for Nonlinear Backward Stochastic Partial Differential Equations and Their Error Estimates. Advances in Applied Mathematics and Mechanics. 12 (6). 1457-1480. doi:10.4208/aamm.OA-2019-0345
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