Error analysis of finite element approximations of the optimal control problem for stochastic Stokes equations with additive white noise
Error analysis of finite element approximations of the optimal control problem for stochastic Stokes equations with additive white noise
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DOI：
10.1016/j.apnum.2018.03.002
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发表时间：
2018-11
影响因子：
2.8
通讯作者：
Young-Pil Choi;Hyung-C. Lee
中科院分区：
文献类型：
--
作者：
Young-Pil Choi;Hyung-C. Lee
研究了强迫项受白色噪声扰动的随机Stokes方程最优控制问题的有限元逼近解。为了获得最有效的确定性最优控制，我们按照[20]中的建议建立了成本泛函。利用绿色函数和Brezzi-Rappaz-Raviart理论建立了完全耦合最优系统的误差估计。数值例子也被用来检验我们的理论结果。
Finite element approximation solutions of the optimal control problems for stochastic Stokes equations with the forcing term perturbed by white noise are considered. To obtain the most efficient deterministic optimal control, we set up the cost functional as we proposed in [20]. Error estimates are established for the fully coupled optimality system using Green's functions and Brezzi–Rappaz–Raviart theory. Numerical examples are also presented to examine our theoretical results.