Error Estimates of Finite Element Methods for the Nonlinear Backward Stochastic Stokes Equations
Year: 2024
Type: article
Abstract: 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.
Authors: Yongwang Sun, Weidong Zhao, Wenju Zhao
Institution: Shandong University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404554584